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Extended Jaynes-Cummings Models In Cavity Qed
KTH, School of Engineering Sciences (SCI), Physics.
2005 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

Due to the improvement within cavity quantum electrodynamics experiments during the last decades, what was former seen as 'toy models' are today realized in laboratories. A controlled isolated coherent evolution of one or a few atoms coupled to a single mode inside a cavity is achievable. Such systems are well suited for studying purely quantum mechanical effects, and also for performing quantum gates, necessary for quantum computing. The Jaynes-Cummings model has served as a theoretical description of the interaction. However, as the experimental techniques are improved, for example, atom cooling, the use of multi-level atoms or multi-modes and driving of atoms or elds by external lasers, extensions of the original Jaynes-Cummings model are needed. In this thesis we study some of these extended models, and in particular multi-level models, time-dependent models and quantized motion models. Both analytical and numerical analysis are considered. The two-level structure of the Jaynes-Cummings model leads to applications of known solvable time-dependent two-level Schrödinger equations. In other cases, di erent forms of adiabatic approximate solutions are used, and with the analytically solvable models, the amplitudes of non-adiabatic contributions may be estimated. For higher dimensional systems, STIRAP and multi-STIRAP methods are applied. It is shown how the time-dependent models may be used for preparation of various kinds of non-classical states, and also to generate universal sets of quantum gates, both on atomic and eld qubits. When the atoms are cooled to very low temperatures, their velocities must be treated quantum mechanically, and we have studied the dynamics of such cases for di erent coupling shapes. Again numerical and analytical approaches have been used and compared, wave-packet propagations of the atom, approaching and traversing the cavity, have been performed. For periodic couplings, standing wave cavity modes, the dynamics has been described by e ective parameters; group velocity or atomic index of refraction and effective mass. Tunneling resonances for ultra cold atoms have been exhibited in the STIRAP models for certain initial conditions.

Place, publisher, year, edition, pages
Stockholm: KTH , 2005. , vii, 86 p.
Series
Trita-FYS, ISSN 0280-316X ; 2005:44
Keyword [en]
Physical chemistry, Optics
National Category
Atom and Molecular Physics and Optics
Identifiers
URN: urn:nbn:se:kth:diva-404ISBN: 91-7178-124-2 (print)OAI: oai:DiVA.org:kth-404DiVA: diva2:10520
Public defence
2005-09-19, Sal FB53, AlbaNova, Roslagstullsbacken 21, Stockholm, 10:00
Opponent
Supervisors
Note
QC 20101027Available from: 2005-09-06 Created: 2005-09-06 Last updated: 2010-10-27Bibliographically approved
List of papers
1. Adiabatic state preparation in a cavity
Open this publication in new window or tab >>Adiabatic state preparation in a cavity
2003 (English)In: Journal of Modern Optics, ISSN 0950-0340, E-ISSN 1362-3044, Vol. 50, no 11, 1663-1678 p.Article in journal (Refereed) Published
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.

National Category
Atom and Molecular Physics and Optics
Identifiers
urn:nbn:se:kth:diva-5962 (URN)10.1080/0950034031000064915 (DOI)000184129700003 ()
Note
QC 20101026Available from: 2005-09-06 Created: 2005-09-06 Last updated: 2010-10-26Bibliographically approved
2. Photon filters in a microwave cavity
Open this publication in new window or tab >>Photon filters in a microwave cavity
2003 (English)In: Journal of Modern Optics, ISSN 0950-0340, E-ISSN 1362-3044, Vol. 50, no 18, 2705-2715 p.Article in journal (Refereed) Published
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.

Keyword
jaynes-cummings model, atomic motion, quantum, states
National Category
Atom and Molecular Physics and Optics
Identifiers
urn:nbn:se:kth:diva-5963 (URN)10.1080/0950034031000095551 (DOI)000187029500001 ()
Note
QC 20101026Available from: 2005-09-06 Created: 2005-09-06 Last updated: 2010-10-26Bibliographically approved
3. Cavity field ensembles from non-selective measurements
Open this publication in new window or tab >>Cavity field ensembles from non-selective measurements
2004 (English)In: Journal of Modern Optics, ISSN 0950-0340, E-ISSN 1362-3044, Vol. 51, no 1, 129-138 p.Article in journal (Refereed) Published
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.

Keyword
quantum, generation, micromaser, states, atoms
National Category
Atom and Molecular Physics and Optics
Identifiers
urn:nbn:se:kth:diva-5964 (URN)10.1080/0950034031000154609 (DOI)000187327600010 ()2-s2.0-0742322097 (Scopus ID)
Note
QC 20101026Available from: 2005-09-06 Created: 2005-09-06 Last updated: 2011-10-31Bibliographically approved
4. Dynamics of a Raman coupled model: entanglement and quantum computation
Open this publication in new window or tab >>Dynamics of a Raman coupled model: entanglement and quantum computation
2004 (English)In: Journal of Modern Optics, ISSN 0950-0340, E-ISSN 1362-3044, Vol. 51, no 11, 1691-1704 p.Article in journal (Refereed) Published
Abstract [en]

The evolution of a Raman coupled three-level Lambda atom with two quantized cavity modes is studied in the large detuning case; i.e. when the upper atomic level can be adiabatically eliminated. Particularly the situation when the two modes are prepared in initial coherent or squeezed states, with a large average number of photons, is investigated. It is found that the atom, after specific interaction times, disentangles from the two modes, leaving them, in certain cases, in entangled Schrodinger cat states. These disentanglement times can be controlled by adjusting the ratio between average numbers of photons in the two modes. It is also shown how this effective model may be used for implementing quantum information processing. Especially it is demonstrated how to generate various entangled states, such as EPR and GHZ states, and quantum logic operations, such as the control-not and the phase gate.

Keyword
jaynes-cummings model, 3-level atom, evolution, fields, states
National Category
Atom and Molecular Physics and Optics
Identifiers
urn:nbn:se:kth:diva-5965 (URN)10.1080/0950034042000200498 (DOI)000222181300010 ()2-s2.0-3142624784 (Scopus ID)
Note
QC 20101026Available from: 2005-09-06 Created: 2005-09-06 Last updated: 2011-09-26Bibliographically approved
5. Cavity-state preparation using adiabatic transfer
Open this publication in new window or tab >>Cavity-state preparation using adiabatic transfer
2005 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 71, no 5Article in journal (Refereed) Published
Abstract [en]

We show how to prepare a variety of cavity field states for multiple cavities. The state preparation technique used is related to the method of stimulated adiabatic Raman passage. The cavity modes are coupled by atoms, making it possible to transfer an arbitrary cavity field state from one cavity to another and also to prepare nontrivial cavity field states. In particular, we show how to prepare entangled states of two or more cavities, such as an Einstein-Podolsky-Rosen state and a W state, as well as various entangled superpositions of coherent states in different cavities, including Schrodinger cat states. The theoretical considerations are supported by numerical simulations.

Keyword
raman-coupled model, population transfer, systems, atoms, light
National Category
Atom and Molecular Physics and Optics
Identifiers
urn:nbn:se:kth:diva-5966 (URN)10.1103/PhysRevA.71.053814 (DOI)000229543600118 ()2-s2.0-26944447148 (Scopus ID)
Note
QC 20101026Available from: 2005-09-06 Created: 2005-09-06 Last updated: 2010-10-26Bibliographically approved
6. Effective mass in cavity QED
Open this publication in new window or tab >>Effective mass in cavity QED
2005 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 72, no 1Article in journal (Refereed) Published
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.

Keyword
jaynes-cummings model, atomic-beam deflection, standing-wave cavity, photon number, single atoms, quantum-theory, motion, states, field, entanglement
National Category
Atom and Molecular Physics and Optics
Identifiers
urn:nbn:se:kth:diva-5967 (URN)10.1103/PhysRevA.72.013814 (DOI)000230887300147 ()2-s2.0-27144469574 (Scopus ID)
Note

QC 20101026

Available from: 2005-09-06 Created: 2005-09-06 Last updated: 2012-09-19Bibliographically approved
7. Level crossings in a cavity QED model
Open this publication in new window or tab >>Level crossings in a cavity QED model
2006 (English)In: Physical Review A. Atomic, Molecular, and Optical Physics, ISSN 1050-2947, E-ISSN 1094-1622, Vol. 73, no 1Article in journal (Refereed) Published
Abstract [en]

In this paper I study the dynamics of a two-level atom interacting with a standing-wave field. When the atom is subjected to a weak linear force, the problem can be turned into a time-dependent one, and the evolution is understood from the band structure of the spectrum. The presence of level crossings in the spectrum gives rise to Bloch oscillations of the atomic motion. Here I investigate the effects of the atom-field detuning parameter. A variety of different level crossings are obtained by changing the magnitude of the detuning, and the behavior of the atomic motion is strongly affected due to this. I also consider the situation in which the detuning is oscillating in time, and its impact on the atomic motion. Wave-packet simulations of the full problem are treated numerically and the results are compared with analytical solutions given by the standard Landau-Zener and the three-level Landau-Zener models.

Keyword
wannier-stark ladders, standing-wave cavity, bloch oscillations, 2-level atom, dynamics, quantum, motion, field, emission
National Category
Atom and Molecular Physics and Optics
Identifiers
urn:nbn:se:kth:diva-5968 (URN)10.1103/PhysRevA.73.013823 (DOI)000235008900178 ()2-s2.0-33144464773 (Scopus ID)
Note
QC 20101026Available from: 2005-09-06 Created: 2005-09-06 Last updated: 2010-10-26Bibliographically approved
8. Scheme for generating entangled states of two field modes in a cavity
Open this publication in new window or tab >>Scheme for generating entangled states of two field modes in a cavity
2006 (English)In: Journal of Modern Optics, ISSN 0950-0340, E-ISSN 1362-3044, Vol. 53, no 13, 1867-1877 p.Article in journal (Refereed) Published
Abstract [en]

This paper considers a two-level atom interacting with two cavity modes with equal frequencies. Applying a unitary transformation, the system reduces to the analytically solvable Jaynes-Cummings model. For some particular field states, coherent and squeezed states, the transformation between the two bare bases, related by the unitary transformation, becomes particularly simple. It is shown how to generate (the highly non-classical) entangled coherent states of the two modes, both in the zero and large detuning cases. An advantage of the zero detuning case is that the preparation is deterministic and no atomic measurement is needed. For the large detuning situation, a measurement is required, leaving the field in either of two orthogonal entangled coherent states.

Keyword
jaynes-cummings model, distinguishable quantum states, coherent states, superpositions, collapse, revival, atom, decoherence, evolution, apparatus
National Category
Atom and Molecular Physics and Optics
Identifiers
urn:nbn:se:kth:diva-5969 (URN)10.1080/09500340600674291 (DOI)000239448000005 ()2-s2.0-33746882501 (Scopus ID)
Note
Uppdaterad från submitted til published: 20101026. QC 20101026Available from: 2005-09-06 Created: 2005-09-06 Last updated: 2010-10-26Bibliographically approved

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