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  • 1. Andersson, Erika
    et al.
    Stenholm, Stig
    KTH, School of Engineering Sciences (SCI), Physics.
    Variational properties of a pumped dynamical system2010In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 81, no 2, p. 022111-Article in journal (Refereed)
    Abstract [en]

    We earlier constructed a generalized entropy concept to show the direction of time in an evolution following from a Markov generator. In such a dynamical system the entity found changes in a monotonic way starting from any initial state of the system. In this article, we generalize the treatment to the case when population is pumped into the system from levels not explicitly considered. These populations then pass through the coupled levels and exit by decay to levels outside the system. We derive the form of the equation of motion and relate it to our earlier treatments. It turns out that the formalism can be generalized to the new situation. Its physically relevant features are demonstrated and the behavior obtained is illustrated by a numerical treatment of the standard two-level system with pumping and relaxation included.

  • 2. Clausen, J
    et al.
    Salo, Janne
    KTH, School of Engineering Sciences (SCI), Physics.
    Akulin, V M
    Stenholm, Stig Torsten
    KTH, School of Engineering Sciences (SCI), Physics.
    Nonclassical dynamics induced by a quantum meter2005In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 72, no 6, p. 062104-Article in journal (Refereed)
    Abstract [en]

    Conventionally, the effect of measurements on a quantum system is assumed to introduce decoherence, which renders the system classical- like. We consider here a microscopic meter, that is, an auxiliary essentially quantum system whose state is measured repeatedly, and show that it can be employed to induce transitions from classical states into inherently quantumlike states. The meter state is assumed to be lost in the environment and we derive a non- Markovian master equation for the dynamic system in the case of nondemolition coupling to the meter; this equation can be cast in the form of an (N-a)th- order differential equation in time, where N-a is the dimension of the meter basis. We apply the approach to a harmonic oscillator coupled to a spin-1/2 2 meter and demonstrate how it can be used to engineer effective Hamiltonian evolution, subject to decoherence induced by the projective meter measurements.

  • 3. Croke, Sarah
    et al.
    Barnett, Stephen M.
    Stenholm, Stig
    KTH, School of Engineering Sciences (SCI), Physics.
    Linear transformations of quantum states2008In: Annals of Physics, ISSN 0003-4916, E-ISSN 1096-035X, Vol. 323, no 4, p. 893-906Article in journal (Refereed)
    Abstract [en]

    This paper considers the most general linear transformation of a quantum state. We enumerate the conditions necessary to retain a physical interpretation of the transformed state: hermiticity, normalization and complete positivity. We show that these can be formulated in terms of an associated transformation introduced by Choi in 1975. We extend his treatment and display the mathematical argumentation in a manner closer to that used in traditional quantum physics. We contend that our approach displays the implications of the physical requirements in a simple and intuitive way. In addition, defining an arbitrary vector, we may derive a probability distribution over the spectrum of the associated transformation. This fixes the average of the eigenvalue independently of the vector chosen. The formal results are illustrated by a couple of examples.

  • 4. Garraway, B. M.
    et al.
    Stenholm, Stig
    KTH, School of Engineering Sciences (SCI), Physics.
    Emergent randomness in the Jaynes-Cummings model2008In: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, ISSN 1751-8113, Vol. 41, no 7, p. 075304-Article in journal (Refereed)
    Abstract [en]

    We consider the well-known Jaynes-Cummings model and ask if it can display randomness. As a solvable Hamiltonian system, it does not display chaotic behaviour in the ordinary sense. Here, however, we look at the distribution of values taken up during the total time evolution. This evolution is determined by the eigenvalues distributed as the square roots of integers and leads to a seemingly erratic behaviour. That this may display a random Gaussian value distribution is suggested by an exactly provable result by Kac. In order to reach our conclusion we use the Kac model to develop tests for the emergence of a Gaussian. Even if the consequent double limits are difficult to evaluate numerically, we find definite indications that the Jaynes-Cummings case also produces a randomness in its value distributions. Numerical methods do not establish such a result beyond doubt, but our conclusions are definite enough to suggest strongly an unexpected randomness emerging in a dynamic time evolution.

  • 5.
    Jakob, Matthias
    et al.
    KTH, Superseded Departments, Physics.
    Stenholm, Stig
    KTH, Superseded Departments, Physics.
    Effects of a thermal reservoir on variational functions in open systems2004In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 70, no 1Article in journal (Refereed)
    Abstract [en]

    We connect the theory of a Lyapunov functional for an open system with the thermophysical concept of the relative entropy or equivalently with the entropy production rate. In order to do this we consider the environment of the open system as a thermal reservoir, which introduces the temperature as a thermophysical quantity. The general theory of the Lyapunov functional of an open system constructs a metric operator which contains an element of ambiguity in its scaling. This ambiguity can be removed by assuming a thermostatistic environment which fixes the scaling of the metric operator in a unique manner. The Lyapunov functional thus acquires a thermophysical meaning and can be connected with a relative entropy. In this case the metric operator is related to the inverse of the stationary density operator of the system. We illustrate the theory on a two-level atomic system and a degenerate three-level atom which are exposed to a thermal electromagnetic environment.

  • 6.
    Jakob, Matthias
    et al.
    KTH, Superseded Departments, Physics.
    Stenholm, Stig
    KTH, Superseded Departments, Physics.
    Variational functions in degenerate open quantum systems2004In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 69, no 4, p. 042105-Article in journal (Refereed)
    Abstract [en]

    We have derived a Lyapunov functional for a degenerate open atomic system. This functional develops monotonically towards its stationary state. The open system is described by a Lindblad-type master equation. For the construction of the variational functional it is necessary that the Lindblad operator can be diagonalized. Since the generator of motion is non-Hermitian, diagonalization is, in general, only possible if the eigenvalues are nondegenerate. In this paper, we propose that in a physical system the biorthogonal eigenbasis of the Lindblad operator remains complete even when degeneracy is present. Thus diagonalization of the Lindblad operator, and consequently the construction of the variational functional, is still possible. We discuss the reasons and illustrate the theory of the variational functional for a driven Lambda-type three-level atom with degenerate ground state. The degeneracy has interesting effects on the variational functional in the steady state with respect to its interpretation as an entropic quantity. In case of the driven three-level atom, the dark state turns out to be an isentropic state.

  • 7. Kajari, E.
    et al.
    Harshman, N. L.
    Rasel, E. M.
    Stenholm, Stig
    KTH, School of Engineering Sciences (SCI), Physics.
    Süssmann, G.
    Schleich, W. P.
    Inertial and gravitational mass in quantum mechanics2010In: Applied physics. B, Lasers and optics (Print), ISSN 0946-2171, E-ISSN 1432-0649, Vol. 100, no 1, p. 43-60Article in journal (Refereed)
    Abstract [en]

    We show that in complete agreement with classical mechanics, the dynamics of any quantum mechanical wave packet in a linear gravitational potential involves the gravitational and the inertial mass only as their ratio. In contrast, the spatial modulation of the corresponding energy wave function is determined by the third root of the product of the two masses. Moreover, the discrete energy spectrum of a particle constrained in its motion by a linear gravitational potential and an infinitely steep wall depends on the inertial as well as the gravitational mass with different fractional powers. This feature might open a new avenue in quantum tests of the universality of free fall.

  • 8. Kis, Z.
    et al.
    Paspalakis, E.
    Renzoni, F.
    Stenholm, Stig Torsten
    KTH, Superseded Departments, Physics.
    Controlling material by light and light by material via adiabatic processes2004In: Acta Physica Hungarica, Series B: Quantum Electronics, ISSN 1589-9535, Vol. 1, no 2/-, p. 161-164Article in journal (Refereed)
    Abstract [en]

    We present a brief overview of our recent research in the field of adiabatic control of quantum mechanical processes. The most striking properties of the schemes that we study are their reliability and robustness, hence, they can be used not only for standard quantum control problems but for quantum computation as well.

  • 9.
    Larson, Jonas
    et al.
    KTH, Superseded Departments, Physics.
    Garraway, B. M.
    Stenholm, Stig
    KTH, Superseded Departments, Physics.
    Transient effects on electron spin observation2004In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 69, no 3, p. 032103-Article in journal (Refereed)
    Abstract [en]

    In an earlier publication we addressed the problem of splitting an electron beam in the Stern-Gerlach experiment. In contrast to arguments put forward in the early days of quantum theory, we concluded that there are no issues of principle preventing the observation of electron spin during free flight. In that paper, however, we considered only a sudden switch off of the separating magnetic field. In this work we consider the possible effects of finite switching times at the beginning and the end of the interaction period. We consider a model where the coupling between the electron and the field is time dependent. As a result of the time dependence, the field also acquires an electric component, but this seems to cause no significant change of our conclusions. On the other hand, the smooth change of the interaction enforces the same longitudinal velocity on the electron both at the beginning and end of the interaction period because of conservation laws; this effect was missing in our earlier calculations. As the electrons are supposed to travel as a beam, this feature helps by restoring the beam quality after the interaction.

  • 10.
    Larson, Jonas
    et al.
    KTH, School of Engineering Sciences (SCI), Physics.
    Salo, Janne
    Stenholm, Stig
    KTH, School of Engineering Sciences (SCI), Physics.
    Effective mass in cavity QED2005In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 72, no 1Article in journal (Refereed)
    Abstract [en]

    We consider propagation of a two-level atom coupled to one electromagnetic mode of a high-Q cavity. The atomic center-of-mass motion is treated quantum mechanically and we use a standing wave shape for the mode. The periodicity of the Hamiltonian leads to a spectrum consisting of bands and gaps, which is studied from a Floquet point of view. Based on the band theory, we introduce a set of effective mass parameters that approximately describe the effect of the cavity on the atomic motion, with the emphasis on one associated with the group velocity and on another one that coincides with the conventional effective mass. Propagation of initially Gaussian wave packets is also studied using numerical simulations and the mass parameters extracted thereof are compared with those predicted by the Floquet theory. Scattering and transmission of the wave packet against the cavity are further analyzed, and the constraints for the effective mass approach to be valid are discussed in detail.

  • 11.
    Larson, Jonas
    et al.
    KTH, Superseded Departments, Physics.
    Stenholm, Stig
    KTH, Superseded Departments, Physics.
    Adiabatic state preparation in a cavity2003In: Journal of Modern Optics, ISSN 0950-0340, E-ISSN 1362-3044, Vol. 50, no 11, p. 1663-1678Article in journal (Refereed)
    Abstract [en]

    The paper discusses the single-mode Jaynes-Cummings model with time-dependent parameters. Solvable models for two-level systems are utilized to consider the changes in the photon distribution effected by the passage of atoms through the cavity. It is suggested that such systems may be used as filters to modify the photon distribution. The effect can be enhanced by repeatedly sending new atoms through the cavity. We show that such filters can cut out either small or large photon numbers. It is also shown that the method can be used to narrow down photon distributions and in this way achieve highly non-classical sub-Poissonian states. Some limitations and applications of the method are presented.

  • 12.
    Larson, Jonas
    et al.
    KTH, Superseded Departments, Physics.
    Stenholm, Stig
    KTH, Superseded Departments, Physics.
    Cavity field ensembles from non-selective measurements2004In: Journal of Modern Optics, ISSN 0950-0340, E-ISSN 1362-3044, Vol. 51, no 1, p. 129-138Article in journal (Refereed)
    Abstract [en]

    We continue our investigations of cavity QED with time-dependent parameters. In this paper we discuss the situation where the state of the atoms leaving the cavity is reduced but the outcome is not recorded. In this case our knowledge is limited to an ensemble description of the results only. By applying the Demkov - Kunike level-crossing model, we show that even in this case, the filtering action of the interaction allows us to prepare a preassigned Fock state with good accuracy. The possibilities and limitations of the method are discussed and some relations to earlier work are presented.

  • 13.
    Larson, Jonas
    et al.
    KTH, Superseded Departments, Physics.
    Stenholm, Stig
    KTH, Superseded Departments, Physics.
    Photon filters in a microwave cavity2003In: Journal of Modern Optics, ISSN 0950-0340, E-ISSN 1362-3044, Vol. 50, no 18, p. 2705-2715Article in journal (Refereed)
    Abstract [en]

    In an earlier paper we concluded that time-dependent parameters in the atom-mode interaction can be utilized to modify the quantum field in a cavity. When an atom shoots through the cavity field, it is expected to experience a trigonometric time dependence of its coupling constant. We investigate the possibilities this offers to modify the field. As a point of comparison we use the solvable Rosen-Zener model, which has parameter dependences roughly similar to the ones expected in a real cavity. We do confirm that by repeatedly sending atoms through the cavity, we can obtain filters on the photon states. Highly non-classical states can be obtained. We find that the Rosen-Zener model is more sensitive to the detuning than the case of a trigonometric coupling.

  • 14.
    Larson, Jonas
    et al.
    KTH, School of Engineering Sciences (SCI), Physics.
    Stenholm, Stig
    KTH, School of Engineering Sciences (SCI), Physics.
    Validity of adiabaticity in cavity QED2006In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 73, no 3, p. 033805-Article in journal (Refereed)
    Abstract [en]

    This paper deals with the concept of adiabaticity for fully quantum mechanical cavity QED models. The physically interesting cases of Gaussian and standing wave shapes of the cavity mode are considered. An analytical approximate measure for adiabaticity is given and compared with numerical wave packet simulations. Good agreement is obtained where the approximations are expected to be valid. Usually for cavity QED systems, the large atom-field detuning case is considered as the adiabatic limit. We, however, show that adiabaticity is also valid, for the Gaussian mode shape, in the opposite limit. Effective semiclassical time-dependent models, which do not take into account the shape of the wave packet, are derived. Corrections to such an effective theory, which are purely quantum mechanical, are discussed. It is shown that many of the results presented can be applied to time-dependent two-level systems.

  • 15.
    Leibscher, Monica
    et al.
    KTH, School of Engineering Sciences (SCI), Physics.
    Stenholm, Stig
    KTH, School of Engineering Sciences (SCI), Physics.
    Transition steering via space-dependent coupling2005In: Decoherence, Entanglement and Information Protection in Complex Quantum Systems / [ed] Akulin, VM; Sarfati, A; Kurizki, G; Pellegrin, S, 2005, Vol. 189, p. 395-410Conference paper (Refereed)
    Abstract [en]

    The transition between electronic energy surfaces of molecules is usually described in the Franck-Condon approximation where the spatial variation of the coupling matrix elements is neglected. In this work we go beyond this approximation and explore the effects of such a variation using a simply parameterized interaction instead of the usually poorly known realistic variations. Moreover, we propose a model that allows us to steer molecular transitions by shaping the space-dependence of the coupling.

  • 16. Maniscalco, S
    et al.
    Piilo, J
    Vitanov, N
    Stenholm, Stig
    KTH, School of Engineering Sciences (SCI), Physics.
    Transient dynamics of linear quantum amplifiers2005In: European Physical Journal D: Atomic, Molecular and Optical Physics, ISSN 1434-6060, E-ISSN 1434-6079, Vol. 36, no 3, p. 329-338Article in journal (Refereed)
    Abstract [en]

    The transient dynamics of a quantum linear amplifier during the transition from damping to amplification regime is studied. The master equation for the quantized mode of the field is solved, and the solution is used to describe the statistics of the output field. The conditions under which a nonclassical input field may retain nonclassical features at the output of the amplifier are analyzed and compared to the results of earlier theories. As an application we give a dynamical description of the departure of the system from thermal equilibrium.

  • 17. Paul, H.
    et al.
    Greenberger, D. M.
    Stenholm, Stig Torsten
    KTH, School of Engineering Sciences (SCI), Applied Physics.
    Schleich, W. P.
    The Stefan-Boltzmann law: two classical laws give a quantum one2015In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. T165, article id 014027Article in journal (Refereed)
    Abstract [en]

    Due to the universality of blackbody radiation the constant in the Stefan-Boltzmann law connecting the energy density and temperature of blackbody radiation is either a universal constant, or built out of several universal constants. Since the Stefan-Boltzmann law follows from thermodynamics and classical electrodynamics this constant must involve the speed of light and the Boltzmann constant. However, a dimensional analysis points to the existence of an additional universal constant not present in the two classical theories giving birth to the Stefan-Boltzmann law. In the most elementary version this constant has the dimension of an action and is thereby proportional to Planck's constant. We point out this unusual phenomenon of the combination of two classical laws creating a quantum law and speculate about its deeper origin.

  • 18. Plimak, L. , I
    et al.
    Stenholm, Stig
    KTH, School of Engineering Sciences (SCI), Applied Physics. Univ Ulm, Inst Quantenphys, D-89069 Ulm, Germany.;KTH, Royal Inst Technol, Phys Dept, Stockholm, Sweden.;HUT, Lab Computat Engn, Espoo, Finland..
    Quantum chains and regularisation of quantum dynamics2018In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 93, no 10, article id 104002Article in journal (Refereed)
    Abstract [en]

    We argue that the origin of ultraviolet divergences in quantum field theory (QFT) may be not in the perturbative expansion, but in the fact that, mathematically, the Heisenberg equations of motion are not properly defined. Divergences similar to those in QFT are shown to exist in seemingly simple quantum problems with parametric Hamiltonians. These divergences may be suppressed by formally replacing the system in question by a quantum chain. The latter is a dynamically regularised system specified by two postulates, imposing conditions on its response properties. The kinematical postulate specifies the linear response, the dynamical postulate extends it to nonlinear dynamics. The kinematical postulate uniquely determines the mathematical environment (quantisation with indefinite metric), hence the term. Using the Klein-Gordon, Gupta-Bleuler and Dirac fields as examples we show that the concept of quantum chain generalises seamlessly to relativistic quantum fields. Perspectives of using quantum chains as regularisation devices in QFT are discussed.

  • 19. Plimak, L. I.
    et al.
    Ivanov, Misha
    Aiello, A.
    Stenholm, S.
    KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.
    Quantum theory of an electromagnetic observer: Classically behaving macroscopic systems and the emergence of the classical world in quantum electrodynamics2015In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 92, no 2, article id 022122Article in journal (Refereed)
    Abstract [en]

    Quantum electrodynamics under conditions of distinguishability of interactingmatter entities, and of controlled actions and back-actions between them, is considered. Such "mesoscopic quantum electrodynamics" is shown to share its dynamical structure with the classical stochastic electrodynamics. In formal terms, we demonstrate that all general relations of the mesoscopic quantum electrodynamics may be recast in a form lacking Planck's constant. Mesoscopic quantum electrodynamics is therefore subject to "doing quantum electrodynamics while thinking classically," allowing one to substitute essentially classical considerations for quantum ones without any loss in generality. Implications of these results for the quantum measurement theory are discussed.

  • 20. Plimak, L. I.
    et al.
    Schleich, W. P.
    Stenholm, Stig T.
    KTH, School of Engineering Sciences (SCI), Physics.
    Causal signal transmission by interacting quantum fields2008In: Proc. Int. Conf. Path Integr.: New Trends Perspect., PI, 2008, p. 152-156Conference paper (Refereed)
    Abstract [en]

    General response properties of interacting bosonic fields are investigated.

  • 21. Plimak, L. I.
    et al.
    Stenholm, Stig
    KTH, School of Engineering Sciences (SCI), Physics.
    Causal signal transmission by quantum fields. I: Response of the harmonic oscillator2008In: Annals of Physics, ISSN 0003-4916, E-ISSN 1096-035X, Vol. 323, no 8, p. 1963-1988Article in journal (Refereed)
    Abstract [en]

    It is shown that response properties of a quantum harmonic oscillator are in essence those of a classical oscillator, and that, paradoxical as it may be, these classical properties underlie all quantum dynamical properties of the system. The results are extended to noninteracting bosonic fields, both neutral and charged.

  • 22. Plimak, L. I.
    et al.
    Stenholm, Stig
    KTH, School of Engineering Sciences (SCI), Physics.
    Causal signal transmission by quantum fields. II: Quantum-statistical response of interacting bosons2008In: Annals of Physics, ISSN 0003-4916, E-ISSN 1096-035X, Vol. 323, no 8, p. 1989-2017Article in journal (Refereed)
    Abstract [en]

    We analyse nonperturbatively signal transmission patterns in Green's functions of interacting quantum fields. Quantum field theory is reformulated in terms of the nonlinear quantum-statistical response of the field. This formulation applies equally to interacting relativistic fields and nonrelativistic models. Of crucial importance is that all causality properties to be expected of a response formulation indeed hold. Being by construction equivalent to Schwinger's closed-time-loop formalism, this formulation is also shown to be related naturally to both Kubo's linear response and Glauber's macroscopic photodetection theories, being a unification of the two with generalisation to the nonlinear quantum-statistical response problem. In this paper we introduce response formulation of bosons; response reformulation of fermions will be subject of a separate paper.

  • 23. Plimak, L. I.
    et al.
    Stenholm, Stig
    KTH, School of Engineering Sciences (SCI), Physics.
    Causal signal transmission by quantum fields. III: Coherent response of fermions2009In: Annals of Physics, ISSN 0003-4916, E-ISSN 1096-035X, Vol. 324, no 3, p. 600-636Article in journal (Refereed)
    Abstract [en]

    Structural response properties of fermionic fields are investigated. in the presence of fermions the key technical concept becomes response combination, or R-normal product, of field operators. It generalises the notion of time-normal operator product to response problems. Time-normal products are a special case of R-normal products without inputs; this paper thus also generalises the concept of time-normal ordering to fermions. Explicit causality of R-normal products of arbitrary (bosonic and/or fermionic) field operators is proven, and explicit relations expressing them by conventional Green's functions of quantum field theory are derived.

  • 24. Plimak, L. I.
    et al.
    Stenholm, Stig
    KTH, School of Information and Communication Technology (ICT), Optics and Photonics, Quantum Electronics and Quantum Optics, QEO (moved to SCI 2011-07-01).
    Causal signal transmission by quantum fields. IV. The causal Wick theorem2011In: Physical Review D, ISSN 1550-7998, E-ISSN 1550-2368, Vol. 84, no 6, p. 065025-Article in journal (Refereed)
    Abstract [en]

    Wick's theorem in the Schwinger-Perel-Keldysh closed-time-loop formalism is written in a form where the place of contractions is taken by the linear response function of the field. This result demonstrates that the physical information supplied by Wick's theorem for operators is propagation of the free field in space and time.

  • 25. Plimak, L. I.
    et al.
    Stenholm, Stig
    KTH, School of Engineering Sciences (SCI), Physics.
    Causal signal transmission by quantum fields. V: Generalised Keldysh rotations and electromagnetic response of the Dirac sea2012In: Annals of Physics, ISSN 0003-4916, E-ISSN 1096-035X, Vol. 327, no 11, p. 2691-2741Article in journal (Refereed)
    Abstract [en]

    The connection between real-time quantum field theory (RTQFT) [see, e.g., A.Kamenev and A.Levchenko, Adv. Phys. 58 (2009) 197] and phase-space techniques [E.Wolf and L.Mandel, Optical Coherence and Quantum Optics (Cambridge, 1995)] is investigated. The Keldysh rotation that forms the basis of RTQFT is shown to be a phase-space mapping of the quantum system based on the symmetric (Weyl) ordering. Following this observation, we define generalised Keldysh rotations based on the class of operator orderings introduced by Cahill and Glauber [K.E. Cahill, R.J. Glauber, Phys.Rev.177 (1969) 1882]. Each rotation is a phase-space mapping, generalising the corresponding ordering from free to interacting fields. In particular, response transformation [L.I.Plimak, S.Stenholm, Ann.Phys. (N.Y.) 323 (2008) 1989] extends the normal ordering of free-field operators to the time-normal ordering of Heisenbergoperators. Structural properties of the response transformation, such as its association with the nonlinear quantum response problem and the related causality properties, hold for all generalised Keldysh rotations.Furthermore, we argue that response transformation is especially suited for RTQFT formulation of spatial, in particular, relativistic, problems, because it extends cancellation of zero-point fluctuations, characteristic of the normal ordering, to interacting fields. As an example, we consider quantised electromagneticfield in the Dirac sea. In the time-normally-ordered representation, dynamics of the field looks essentially classical (fields radiated by currents), without any contribution from zero-point fluctuations. For comparison, we calculate zero-point fluctuations of the interacting electromagneticfield under orderings other than time-normal. The resulting expression is physically inconsistent: it does not obey the Lorentz condition, nor Maxwell's equations.

  • 26. Plimak, L. I.
    et al.
    Stenholm, Stig
    KTH, School of Engineering Sciences (SCI), Physics.
    Causal signal transmission by quantum fields. VI: The Lorentz condition and Maxwell's equations for fluctuations of the electromagnetic field2013In: Annals of Physics, ISSN 0003-4916, E-ISSN 1096-035X, Vol. 338, p. 207-249Article in journal (Refereed)
    Abstract [en]

    The general structure of electromagnetic interactions in the so-called response representation of quantum electrodynamics(QED)is analysed. A formal solution to the general quantum problem of the electromagnetic fieldinteracting with matter is found. Independently, a formal solution to the corresponding problem in classical stochastic electrodynamics(CSED)is constructed. CSED and QED differ only in the replacement of stochastic averages of c-number fields and currents by time-normal averages of the corresponding Heisenbergoperators. All relations of QED connecting quantum field to quantum current lack Planck's constant, and thus coincide with their counterparts in CSED. In Feynman's terms, one encounters complete disentanglement of the potential and current operators in response picture.

  • 27. Plimak, L. I.
    et al.
    Stenholm, Stig Torsten
    KTH, School of Engineering Sciences (SCI), Physics.
    Operator ordering and causality beyond the rotating wave approximation2011In: Europhysics letters, ISSN 0295-5075, E-ISSN 1286-4854, Vol. 96, no 3, p. 34002-Article in journal (Refereed)
    Abstract [en]

    Conventional definition of the time-normal operator ordering (KELLEY P. L. and KLEINER W. H., Phys. Rev., 136 (1964) A316) is prone to causality violations (de HAAN M., Physica A, 132 (1985) 375; 397). We show that such violations disappear if this definition is amended outside the rotating wave approximation. Nonrelativistic causality of an arbitrary time-normal product turns out to be a property of quantum kinematics, while relativistic causality is demonstrated for a time-normal product of two operators under the most general assumptions about quantum dynamics (commutativity of operators at space-like intervals). This eliminates the key obstacle preventing phase-space techniques of quantum optics from being extended to arbitrary quantum fields including fermions.

  • 28. Plimak, L. I.
    et al.
    Stenholm, Stig Torsten
    KTH, School of Engineering Sciences (SCI), Physics.
    Schleich, W. P.
    Operator ordering and causality2012In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. T147, p. 014026-Article in journal (Refereed)
    Abstract [en]

    A formal implementation of the concepts of mesoscopic electromagnetic interaction and of the propagating wave in quantum electrodynamics beyond the rotating wave approximation is discussed. Used as a guide, these concepts lead to a natural resolution of a long-standing controversy: causality violations in the Glauber-Kelley-Kleiner photodetection theory. The Glauber-Kelley-Kleiner definition of the time-normal operator ordering must be amended without the rotating wave approximation, which eliminates all causality problems.

  • 29. Praxmeyer, Ludmila
    et al.
    Stenholm, Stig
    KTH, School of Engineering Sciences (SCI), Physics.
    Vitanov, Nikolay
    Characteristics of a pure-state ambiguity function2009In: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, ISSN 1751-8113, Vol. 42, no 49, p. 495301-Article in journal (Refereed)
    Abstract [en]

    We present the necessary and sufficient condition for a square integrable function on R-2N to be an ambiguity function corresponding to a square integrable function on R-N. This condition has the form of an integral equation. We also list some easier to check necessary conditions that must be fulfilled by a function that is an ambiguity function of a pure state. We show how to construct a wavefunction corresponding to a given ambiguity function and we present examples of how our formal results can be used in practice.

  • 30. Praxmeyer, Ludmila
    et al.
    Stenholm, Stig
    KTH, School of Engineering Sciences (SCI), Physics.
    Vitanov, Nikolay V.
    The information of ambiguity2009In: Journal of Modern Optics, ISSN 0950-0340, E-ISSN 1362-3044, Vol. 56, no 10, p. 1205-1219Article in journal (Refereed)
    Abstract [en]

    The phase space characteristics of a quantum state are best captured by the Wigner distribution. This displays transparently the diagonality information of the density matrix. The complementary function offering transparently the off-diagonal elements is captured by a function called the S-function, or the ambiguity. In carrying the maximal information about the quantum coherences it represents the uncertainties or ambiguity of the diagonal information. Mathematically this is manifested in its role as the phase space moment generating function. Formally it complements the information in the Wigner function. These formal relations provide the starting point for the present investigations. As a measure of quantum uncertainties, ambiguity may be used to define a probability measure on the off-diagonality. The mathematical and physical consistency of this view is presented in this paper. For a pure state, we find the extraordinary result that such distributions are their own Fourier transforms. The physical interpretation of this distribution as a carrier of classical signal fuzziness suggests the introduction of heuristic approximations to the observational uncertainties. We illustrate the properties and interpretation of the ambiguity function by some specific examples. We find that for smooth, 'Gaussian-like' distributions, the heuristic considerations provide good approximations. On the other hand, representing quantum interferences, the ambiguity serves as the most positive probe for the ultimate quantum structures which have been called sub-Planckian. They are interesting because it has been argued that such structures are physically observable.

  • 31.
    Salo, Janne
    et al.
    KTH, School of Engineering Sciences (SCI), Physics.
    Barnett, S. M.
    Stenholm, Stig
    KTH, School of Engineering Sciences (SCI), Physics.
    Non-Markovian thermalisation of a two-level atom2006In: Optics Communications, ISSN 0030-4018, E-ISSN 1873-0310, Vol. 259, no 2, p. 772-780Article in journal (Refereed)
    Abstract [en]

    We consider thermalisation and spontaneous decay of a two-level atom beyond the Markovian approximation. While the standard elimination of the continuum of radiation modes results in exponential decay represented by a Lindblad equation of motion, we use a simple toy model that takes into account the finite relaxation rate of the environment and present an exact non-Markovian master equation of the Nakajima-Zwanzig form. Because the exact derivation of non-Markovian equations has proved very difficult for all more realistic (and hence much more complicated) models, we analyze the master equation obtained and also discuss difficulties that are likely to arise with non-Markovian evolution operators.

  • 32.
    Salo, Janne
    et al.
    KTH, School of Engineering Sciences (SCI), Physics.
    Stenholm, Stig
    KTH, School of Engineering Sciences (SCI), Physics.
    Kurizki, G.
    Kofman, A. G.
    The varieties of Master Equations2005In: Decoherence, Entanglement and Information Protection in Complex Quantum Systems / [ed] Akulin, VM; Sarfati, A; Kurizki, G; Pellegrin, S, DORDRECHT: SPRINGER , 2005, Vol. 189, p. 239-280Conference paper (Refereed)
    Abstract [en]

    Irreversible time evolution is in quantum systems described by Master Equations. These are usually derived by elimination of degrees of freedom belonging to an environment acting as a reservoir. When the reservoir is acting as a sink for information, it has got no memory, we obtain equations usually termed Markovian. In this limit it has been shown by semi-group arguments which form preserves all physically relevant properties of the quantum state. It has been noted that not all Markovian equations derived lead to physically meaningful conclusions. On the other hand, the derivations prove that exact equations can be obtained if the memory effects are retained. We have also observed that improper introduction of the memory features may lead to unphysical results. We pose the challenge to find the general criteria which guarantee that the time evolution described by a density matrix is physically acceptable. However, it is also possible to avoid memory problems by deriving an equation of motion with time dependent coefficients, a so called memory-less Master Equation. In order to apply the same considerations on more complicated models one runs into problems posed by the formal structure of the method. Thus we warn against ad hoc applications of irreversible Master Equations. We explain the properties and emergence of these features with the scope of simple models which can be analysed properly; thus we hope to provide some insight into the character of irreversible time evolution. First we consider an exactly solvable model in which a two-level atom is allowed to decay into a thermally relaxing reservoir, represented by another two-level atom (so-called faked continuum model). Memory equations are, however, highly dependent on the form of memory functions and even a slight inisparameterisation leads to non-positive. evolution. As an alternative to the foregoing approach, we outline the derivation of a generalised non-Markovian equation for a two-level system that is coupled to a finite-temperature bath and driven by an arbitrary time-dependent field. This derivation does not invoke the rotating-wave approximation and yields dynamically-modified rates for population decay and decoherence.

  • 33.
    Stenholm, Stig
    KTH, School of Engineering Sciences (SCI), Physics.
    Beyond the Jaynes-Cummings model2013In: Journal of Physics B: Atomic, Molecular and Optical Physics, ISSN 0953-4075, E-ISSN 1361-6455, Vol. 46, no 22, p. 224013-Article in journal (Refereed)
    Abstract [en]

    The Jaynes-Cummings model is approached as a single-mode case of the solvable Lee model. This model can be treated for all mode numbers up to the continuum limit, which encompasses various adiabatic processes, finite renormalization and the emergence of irreversible time evolution.

  • 34.
    Stenholm, Stig
    KTH, School of Engineering Sciences (SCI), Physics.
    Entanglement of Pure States2009In: Foundations of physics, ISSN 0015-9018, E-ISSN 1572-9516, Vol. 39, no 6, p. 642-655Article in journal (Refereed)
    Abstract [en]

    We consider the concept of entanglement for pure cases of finite dimensional state spaces. The criterion of unentangled states is related to demanding rank one of an associated eigenvalue problem. In addition to the conventional procedure based on the Schmidt decomposition, we devise a method based on the spectral resolution of unsymmetric matrices. In particular, we consider the case when all eigenvalues are zero, and find that the method still works.

  • 35.
    Stenholm, Stig
    KTH, School of Engineering Sciences (SCI), Physics.
    Information and two-level systems2006In: Optics Communications, ISSN 0030-4018, E-ISSN 1873-0310, Vol. 264, no 2, p. 385-392Article in journal (Refereed)
    Abstract [en]

    I consider the general functions depending on the quantum state represented by a two-level density matrix. Quantities of relevance are state distance and informations measures, i.e. entropies. I introduce a new complex representation of such functions. Utilizing the geometric interpretation of complex mappings, I summarize several properties of such transformations of the state. In particular these results are used to suggest several possible applications to physical questions. These are tentative only, but they indicate the physical relevance of the mathematical results presented.

  • 36.
    Stenholm, Stig
    KTH, Superseded Departments, Physics.
    Irreversibility, time reversal and generalised entropy2004In: Quantum Communication, Measurement And Computing / [ed] Barnett, SM; Andersson, E; Jeffers, J; Ohberg, P; Hirota, O, 2004, Vol. 734, p. 383-386Conference paper (Refereed)
    Abstract [en]

    In a series of papers, we have discussed the dynamics of an open system. These describe the general situation when time irreversibility is involved [1]. If the system lacks memory, the evolution describes a semi group, and the general form of the corresponding infinitesimal generator was given by Gorini, Kossakowski and Sudarshan for finite dimensional state spaces [2] and for bounded operators by Lindblad [3]. Here we assume the evolution to be of this type. The general theory we present is based on the work [4] and the references there in. Here I summarize the theory in Sec. 2 and apply it to a communication situation in See. 3. This is modelled on the quantum scattering theory [7]. The response of a quantum optical system has earlier been formulated in terms of input and output states, see e.g. [8] and [9]; for a discussion see [10].

  • 37.
    Stenholm, Stig
    KTH, School of Engineering Sciences (SCI), Physics.
    On entropy production2008In: Annals of Physics, ISSN 0003-4916, E-ISSN 1096-035X, Vol. 323, no 11, p. 2892-2904Article in journal (Refereed)
    Abstract [en]

    We investigate the case of a dynamical system when irreversible time evolution is generated by a nonHermitian superoperator on the states of the system. We introduce a generalized scalar product which can be used to construct a monotonically changing functional of the state, a generalized entropy. This will depend on the level of system dynamics described by the evolution equation. In this paper we consider the special case when the irreversibility derives from imbedding the system of interest into a thermal reservoir. The ensuing time evolution is shown to be compatible both with equilibrium thermodynamics and the entropy production near the final steady state. In particular, Prigogine's principle of minimum entropy production is discussed. Also the limit of zero temperature is considered. We present comments on earlier treatments.

  • 38.
    Stenholm, Stig
    KTH, School of Engineering Sciences (SCI), Physics.
    Radical operationalism2010In: PHYSICA SCRIPTA    , 2010, Vol. T140, p. 014001-Conference paper (Other academic)
    Abstract [en]

    We discuss the practice of quantum theory as a mechanism to obtain probabilistic predictions only. Deciding on which physical entity to measure, we can only derive predictions for the statistics of lists of recorded observations. The state vector carries information about preparation determining the state of every member of the corresponding ensemble. If we accept this as the only product of the formalism, we can draw no definite conclusions about the reality entailing the use of such a state vector. When observed outcomes relate to combined quantum systems, the probabilistic character of the theory offers what has been interpreted as a specific quantum nonlocality. It is argued that this conclusion is unwarranted. A strict adherence to the Copenhagen view makes the nonlocality emerge from the character of knowledge as probabilistic only. Such a knowledge will condition measurements independently of where and when the knowledge is acquired. There exists a primary probability, as a basic trait of nature itself, that has nothing to do with the observer's knowledge or ignorance. Hermann Weyl on Quantum Theory

  • 39.
    Stenholm, Stig
    KTH, School of Engineering Sciences (SCI), Physics.
    The Construction of Quantum Reality2012In: Foundations of physics, ISSN 0015-9018, E-ISSN 1572-9516, Vol. 42, no 1, p. 86-97Article in journal (Refereed)
    Abstract [en]

    This paper recognizes that quantum theory is not satisfactorily formulated; in spite of its empirical success, we may wish to consider the possibility to find more intuitively acceptable foundations. It is emphasized that the difference between classical physics and quantum theory lies in the fact that the latter depends in an essential way on classical descriptions of the observations from preparation to recording. In addition, only statistical predictions are possible. We discuss the case of entangled quantum systems. Performing an experiment on one subsystem, we move a realized prediction to be a precondition for subsequent observations. The quantum features presented do not fit into a unified interpretation, they are found to be incompletely defined but pragmatically applied. No uniquely well defined interpretation is adequate for all cases.

  • 40.
    Stenholm, Stig
    KTH, School of Engineering Sciences (SCI), Physics.
    The Interpretation of Quantum Mechanics2009In: FOUNDATIONS OF PROBABILITY AND PHYSICS - 5 / [ed] Accardi L; Adenier G; Fuchs CA; Jaeger G; Khrennikov A; Larsson JA; Stenholm S, 2009, Vol. 1101, p. 186-191Conference paper (Refereed)
    Abstract [en]

    This paper approaches the interpretation of Quantum Mechanics as a set of directions for use and draws conclusions concerning its description of reality. It is argued that both the individual state function and the quantum information acquired by an observer are features of reality.

  • 41.
    Stenholm, Stig
    KTH, School of Engineering Sciences (SCI), Physics.
    The multifarious quantum information2006In: Quantum Information Processing, ISSN 1570-0755, E-ISSN 1573-1332, Vol. 5, no 6, p. 481-502Article in journal (Refereed)
    Abstract [en]

    This paper considers the scope and possibilities of quantum information within the consensus interpretation of the theory. It is pointed out that a prepared quantum state offers a multitude of answers determined by the query directed to it. It predicts the outcome of measurements of alternative observations or allows the performance of a selection of quantum information processes. Knowing the state does not determine which observables can be assigned values, but defining a point of view of the observer allows him to derive outcomes of measurements. However, all predictions are in the form of statistical distributions or correlations between observations. Thus they are intrinsically independent of separations in space and time: like all statistical knowledge they have to be reassessed when new infomation imposes a new initial state. Many properties determined by quantum observations must be assigned to the results of the measurements and not to the physical system itself. Thus the property of nonlocality is a consequence of the probabilistic interpretation only, and it corresponds to no feature assigned to the physical reality.

  • 42.
    Stenholm, Stig
    KTH, School of Engineering Sciences (SCI), Physics.
    The multifarious role of entropy2012In: Foundations of Probability and Physics-6 / [ed] DAriano, M; Fei, SM; Haven, E; Hiesmayr, B; Jaeger, G; Khrennikov, A; Larsson, JA, 2012, p. 335-342Conference paper (Refereed)
    Abstract [en]

    I consider the emergence of novel physical concepts in the acquisition of knowledge. Here the entropy plays a centraal role bot to define the most likely situations and their evolution with time.

  • 43.
    Stenholm, Stig
    KTH, School of Engineering Sciences (SCI), Physics.
    Topics in adiabaticity2005In: Laser physics, ISSN 1054-660X, E-ISSN 1555-6611, Vol. 15, no 10, p. 1421-1427Article in journal (Refereed)
    Abstract [en]

    This paper presents the general framework for adiabatic time evolution. It discusses two cases where systematic sequences of approximations are possible: the time-dependent two-level system and the harmonic oscillator with drifting frequency. In the former case, the appearance of a level crossing leads to nonanalytic corrections not captured by the systematic expansion.

  • 44.
    Stenholm, Stig
    KTH, School of Engineering Sciences (SCI), Physics.
    What little we remember2011In: AIP CONF PROC, 2011, Vol. 1327, p. 231-239Conference paper (Refereed)
    Abstract [en]

    The status of phenomenological models is considered and it is argued that they should not be taken as approximations to more fundamental treatments only. To be useful they should work in a consistent world of concepts and their observational manifestations. In this situation, the border between phenomenological theories and fundamental laws is blurred. Within these frames, we discuss the derivations of irreversible master equations when memory effects are significant. In schematic frameworks of derivations, the emergence of irreversibility is followed, and various levels of approximations are presented. Full memory and time-local forms are considered before the Markovian result emerges. The validity of the approximations is discussed.

  • 45.
    Stenholm, Stig
    KTH, School of Engineering Sciences (SCI), Physics.
    When is an entropy an entropy?: Reconsideration of Foundations - 32006In: Quantum Theory: Reconsideration of Foundations - 3 / [ed] Adenier, G; Khrennikov, AY; nieuwenhuizen, TM, MELVILLE, NY: AMER INST PHYSICS , 2006, Vol. 810, p. 263-270Conference paper (Refereed)
    Abstract [en]

    I consider the conceptual arguments leading to the validity of the conventional physical approach to thermodynamics, as we know it. In spite of the familiarity we have with this approach, its internal logical structure deserves to be extracted. No new features are found, but some universal properties emerge. These are then applied to the unconventional system of a black hole, and its thermodynamic description is considered in view of the universal framework presented. It is found that the black hole is highly exceptional, and its thermodynamics contains some unexpected and questionable results. We also discuss the role of entropy as residual indeterminess when a physical system is described by a reduced theory.

  • 46.
    Stenholm, Stig
    et al.
    KTH, Superseded Departments, Physics.
    Jakob, Matthias
    KTH, Superseded Departments, Physics.
    Open systems and time reversal2004In: Journal of Modern Optics, ISSN 0950-0340, E-ISSN 1362-3044, Vol. 51, no 6-7, p. 841-850Article in journal (Refereed)
    Abstract [en]

    In this paper we address the question of the direction of physical time. In particular we consider the meaning of time reversal for irreversible evolution. The work is based on the theory of Markovian generators in open quantum systems. The motivation and appearance of such evolution is reviewed and its implications for the direction of time are presented. A monotonically changing function, a Lyapunov functional, is demonstrated and the concept of time reversal invariance is introduced. Finally the evolution is shown to follow from an action principle. The method, however, does not single out any forward direction of time, information about the initial state is lost equally in both directions within the formalism.

  • 47.
    Stenholm, Stig
    et al.
    KTH, Superseded Departments, Physics.
    Jakob, Matthias
    KTH, Superseded Departments, Physics.
    Time inversion in dynamical systems2004In: Annals of Physics, ISSN 0003-4916, E-ISSN 1096-035X, Vol. 310, no 1, p. 106-126Article in journal (Refereed)
    Abstract [en]

    We consider the case of a dynamical system when the time evolution is generated by a non-hermitian superoperator on the states of the system. Assuming the left and right eigenvectors of this to provide complete basis sets, we propose a generalized scalar product which can be used to construct a monotonically changing functional of the state, a generalized entropy. Combining the time-dependent state with its time-reversed counterpart we can define the operation of time inversion even in this case of irreversible evolution. We require that both the forward and reversed time evolution can be obtained from a generalized action principle, and this demand serves to define the form of the time-reversed state uniquely. The work thus generalizes the quantum treatment from the unitary case to the irreversible one. We present a discussion of the approach and derive some of the direct consequences of our results.

  • 48.
    Stenholm, Stig
    et al.
    KTH, School of Engineering Sciences (SCI), Physics. HUT, Finland .
    Suominen, Kalle-Antti
    Quantum Approach to Informatics2005Book (Other academic)
    Abstract [en]

    An essential overview of quantum information. Information, whether inscribed as a mark on a stone tablet or encoded as a magnetic domain on a hard drive, must be stored in a physical object and thus made subject to the laws of physics. Traditionally, information processing such as computation occurred in a framework governed by laws of classical physics. However, information can also be stored and processed using the states of matter described by non-classical quantum theory. Understanding this quantum information, a fundamentally different type of information, has been a major project of physicists and information theorists in recent years, and recent experimental research has started to yield promising results. Quantum Approach to Informatics fills the need for a concise introduction to this burgeoning new field, offering an intuitive approach for readers in both the physics and information science communities, as well as in related fields. Only a basic background in quantum theory is required, and the text keeps the focus on bringing this theory to bear on contemporary informatics. Instead of proofs and other highly formal structures, detailed examples present the material, making this a uniquely accessible introduction to quantum informatics. Topics covered include: An introduction to quantum information and the qubit. Concepts and methods of quantum theory important for informatics. The application of information concepts to quantum physics. Quantum information processing and computing. Quantum gates. Error correction using quantum-based methods. Physical realizations of quantum computing circuits. A helpful and economical resource for understanding this exciting new application of quantum theory to informatics, Quantum Approach to Informatics provides students and researchers in physics and information science, as well as other interested readers with some scientific background, with an essential overview of the field.

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