Typically, quantum superpositions, and thus measurement projections of quantum states involving interference, decrease (or increase) monotonically as a function of increased distinguishability. Distinguishability, in turn, can be a consequence of decoherence, for example caused by the (simultaneous) loss of excitation or due to inadequate mode matching (either deliberate or indeliberate). It is known that for some cases of multi-photon interference a non-monotonic decay of projection probabilities occurs, which has so far been attributed to interference between four or more photons. We show that such a non-monotonic behavior of projection probabilities is not unnatural, and can also occur for single-photon and even semiclassical states. Thus, while the effect traces its roots from indistinguishability and thus interference, the states for which this can be observed do not need to have particular quantum features.

The algebra of SU(2) is ubiquitous in physics, applicable both to the atomic spin states and the polarisation states of light. The method developed by Majorana and Schwinger to represent pure, symmetric spin-states of arbitrary value as a product of spin-1/2 states is a powerful tool that allows for a great conceptual and practical simplification. Foremost, it allows the representation of a qudit on the same geometry as a qubit, i.e., the Bloch sphere.

An experimental implementation of the Majorana representation in the realm of quantum optics is presented. The technique allows the projection of arbitrary quantum states from a coherent state input. It is also shown that the method can be used to synthesise arbitrary interference patterns with unit visibility, and without resorting to quantum resources. In this context, it is argued that neither the shape nor the visibility of the interference pattern is a good measure of quantumness. It is only the measurement scheme that allows for the perceived quantum behaviour.

The Majorana representation also proves useful in delineating uncertainty limits of states with a particular spin value. Issues with traditional uncertainty relations involving the SU(2) operators, such as trivial bounds for certain states and non-invariance, are thereby resolved with the presented pictorial solution.

KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.

Bjork, Gunnar

KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.

SU(2) uncertainty limits2016In: PHYSICAL REVIEW A, ISSN 2469-9926, Vol. 93, no 5, article id 052101Article in journal (Refereed)

Abstract [en]

Although progress has been made recently in defining nontrivial uncertainty limits for the SU(2) group, a description of the intermediate states bound by these limits remains lacking. In this paper we enumerate possible uncertainty relations for the SU(2) group that involve all three observables and that are, moreover, invariant under SU(2) transformations. We demonstrate that these relations however, even taken as a group, do not provide sharp, saturable bounds. To find sharp bounds, we systematically calculate the variance of the SU(2) operators for all pure states belonging to the N = 2 and N = 3 polarization excitation manifold (corresponding to spin 1 and spin 3/2). Lastly, and perhaps counter to expectation, we note that even pure states can reach the maximum uncertainty limit.

We discuss how to use coincidence detection to generate unusual, nonsinusoidal interference curves by using not a single detector, but several in coincidence. The method works for both strong (classical) and weak (on the fewphoton level) light, although in the latter case the detection becomes probabilistic with low efficiency. Using the method, one can tailor the coincidence measurement setup to obtain essentially any interference pattern. We then use the method to experimentally demonstrate phase-difference state interference patterns in the few-photon regime that are highly nonsinusoidal. We also discuss optimal implementation of the method with regard to fluctuations and success probability, and we analyze the origin and magnitude of errors.

KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.

Swillo, Marcin

KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.

Björk, Gunnar

KTH, School of Engineering Sciences (SCI), Applied Physics, Quantum Electronics and Quantum Optics, QEO.

Synthesis of arbitrary interference patterns with high visibility2013In: 2013 Conference on Lasers and Electro-Optics Europe and International Quantum Electronics Conference, CLEO/Europe-IQEC 2013, IEEE Computer Society, 2013, p. 6801668-Conference paper (Refereed)

Abstract [en]

In recent years there have been many demonstrations of phase super-resolution - previously thought to be a manifestly quantum phenomenon - using classical light [1, 2], but at the expense of reduced interference visibility [3]. It is therefore of interest to delineate what interference effects belong to the realm of classical world, and which require quantum states. Generalizing Hofmann's method of post-selection projection [4], we show that essentially any interference curve can be synthesized with high visibility with coherent state input. The method is based on the mathematical observation that any polynomial can be completely factored over the field of complex numbers. Hence, any two-mode, N-photon state can be written as a product of N single-photon, two-mode states, and the corresponding measurement projector can be experimentally implemented using beam splitters, phase-shifters, and N-photon coincidence measurements.

Using coherent states, linear optics, and N-photon detection we demonstrate the synthesis of arbitrary interference patterns and establish that neither the shape nor the visibility of N-photon interference patterns can be used as a quantum signature in general. Specific examples include saw-curve and rectangle-curve interference patterns and phase super-resolution with period shortening of up to 60 times compared to ordinary interference. The former two have visibility close to 100% and the latter has visibility in excess of 57%.