The paper solves the problem of continuum limit in bosonic thermal coherent-state path integrals. For this purpose, exact discrete versions of the path integral are constructed for three different orderings of the Hamiltonian: normal, anti-normal and symmetric (Weyl order). Subsequently, their different continuum versions are checked on the harmonic oscillator, to choose the symmetric ordering as a possibly correct choice for all polynomial Hamiltonians. Spotted mathematical subtleties in the simple case serve as a clue to the general solution. Finally, a general justification for the symmetric order is provided by deriving the continuum path integral starting from the exact discrete case using a renormalization procedure in the imaginary time frequency domain. While the role of Weyl order has already been found, the paper provides the missing proof of its suitability for every polynomial Hamiltonian and simplifies the previously established construction by referring only to creation and annihilation operators (without position and momentum operators).
We experimentally map the transverse profile of diffraction-limited beams using photon-number-resolving detectors. We observe strong compression of diffracted beam profiles for high detected photon number. This effect leads to higher contrast than a conventional irradiance profile between two Airy disk-beams separated by the Rayleigh criterion.
The discrimination of non-orthogonal quantum states with reduced or without errors is a fundamental task in quantum measurement theory. In this work, we investigate a quantum measurement strategy capable of discriminating two coherent states probabilistically with significantly smaller error probabilities than can be obtained using non-probabilistic state discrimination. We find that appropriate postselection of the measurement data of a photon number resolving detector can be used to discriminate two coherent states with small error probability. We compare our new receiver to an optimal inter…
We experimentally demonstrate a new measurement scheme for the discrimination of two coherent states. The measurement scheme is based on a displacement operation followed by a photon number resolving detector, and we show that it outperforms the standard homodyne detector which we, in addition, proof to be optimal within all Gaussian operations including conditional dynamics. We also show that the non-Gaussian detector is superior to the homodyne detector in a continuous variable quantum key distribution scheme.
We investigate quantum measurement strategies capable of discriminating two coherent states probabilistically with significantly smaller error probabilities than can be obtained using non- probabilistic state discrimination. We apply a postselection strategy to the measurement data of a homodyne detector as well as a photon number resolving detector in order to lower the error probability. We compare the two different receivers with an optimal intermediate measurement scheme where the error rate is minimized for a fixed rate of inconclusive results. The photon number resolving (PNR) receiver i…
There has been much recent interest in quantum optical interferometry for applications to metrology, sub-wavelength imaging, and remote sensing, such as in quantum laser radar (LADAR). For quantum LADAR, atmospheric absorption rapidly degrades any quantum state of light, so that for high-photon loss the optimal strategy is to transmit coherent states of light, which suffer no worse loss than the Beer law for classical optical attenuation, and which provides sensitivity at the shot-noise limit. This approach leaves open the question -- what is the optimal detection scheme for such states in ord…
We put forward a hybrid quantum key distribution protocol based on coherent states, Gaussian modulation, and photon-number-resolving (PNR) detectors, and show that it may enhance the secret key generation rate (KGR) compared to homodyne-based schemes. Improvement in the KGR may be traced back to the dependence of the two-dimensional discrete output variable on both the input quadratures, thus overcoming the limitations of the original protocol. When reverse reconciliation is considered, the scheme based on PNR detectors outperforms the homodyne one both for individual and collective attacks. I…
There has been much recent interest in quantum metrology for applications to sub-Raleigh ranging and remote sensing such as in quantum radar. For quantum radar, atmospheric absorption and diffraction rapidly degrades any actively transmitted quantum states of light, such as N00N states, so that for this high-loss regime the optimal strategy is to transmit coherent states of light, which suffer no worse loss than the linear Beer's law for classical radar attenuation, and which provide sensitivity at the shot-noise limit in the returned power. We show that coherent radar radiation sources, coupl…
We present a method for the experimental measurement of nonclassicality witnesses and demonstrate its application. Our proposal only requires the coherent displacement of the initial state, which can be achieved by overlapping the latter with a coherent state at a beam splitter, and subsequent photon-number resolved detection. This setup allows a complete test of nonclassicality of an arbitrary quantum state. The role of the quantum efficiency as well as statistical and systematic uncertainties are discussed. Finally, the scheme is demonstrated for a realistic example.
The Schroedinger equation with scalar and vector potentials is the continuum limit of any coherent hopping process (where position eigenstates superpose with neighbouring eigenstates after a time step) whose hopping amplitudes are homogeneous in quadratic order of the inverse lattice spacing, inhomogeneous in first order, and satisfying a summability condition with respect to higher-than-next neighbours.
The variance of difference of photocounts (VDPs) is an established measure of quantum correlations for quantum states of light. It enables us to discriminate between the classical correlation of a two-mode coherent state and the quantum correlation of a twin-beam state. We study the effect of loss and saturation of the photon-number-resolving detector on the measurement of the VDPs. An analytic function is derived for this variance, both for the coherent and the twin-beam states. It is found that the VDPs is no longer a reliable entanglement measure in the nonlinear regime of the detector resp…
Interference of light fields plays an important role in various high-precision measurement schemes. It has been shown that super resolving phase measurements beyond the standard coherent state limit can be obtained either by using maximally entangled multi-particle states of light or using complex detection approaches. Here we show that super resolving phase measurements at the shot noise limit can be achieved without resorting to non-classical optical states or to low-efficiency detection processes. Using robust coherent states of light, high-efficiency homodyne detection and a deterministic …
We discuss the time-continuous path integration in the coherent states basis in a way that is free from inconsistencies. Employing this notion we reproduce known and exact results working directly in the continuum. Such a formalism can set the basis to develop perturbative and non-perturbative approximations already known in the quantum field theory community. These techniques can be proven useful in a great variety of problems where bosonic Hamiltonians are used.
We present a new method for the consistent construction of time-continuous coherent-state path integrals using the theory of half-form quantization. Through the inversion of the quantization procedure we construct a de-quantization map taking first order operators to their corresponding path integrals. We generalize our results using functional techniques, allowing for the consistent path integral study of more general operators, including higher orders and interactions.
We define the time-continuous spin coherent-state path integral in a way that is free from inconsistencies. The proposed definition is used to reproduce known exact results. Such a formalism opens new possibilities for applying approximations with improved accuracy and can be proven useful in a great variety of problems where spin Hamiltonians are used.
We have created heralded coherent state superpositions (CSS), by subtracting up to three photons from a pulse of squeezed vacuum light. To produce such CSSs at a sufficient rate, we used our high-efficiency photon-number-resolving transition edge sensor to detect the subtracted photons. This is the first experiment enabled by and utilizing the full photon-number-resolving capabilities of this detector. The CSS produced by three-photon subtraction had a mean photon number of 2.75 -0.24/+0.06 and a fidelity of 0.59 -0.14/+0.04 with an ideal CSS. This confirms that subtracting more photons result…
It is shown that two fundamentally different phenomena, the bound states in continuum and the spectral singularity (or time-reversed spectral singularity), can occur simultaneously. This can be achieved, in particular, in a rectangular core dielectric waveguide with embedded active (or absorbing) layer. In such a system a two-dimensional bound state in a continuum is created in the plane of a waveguide cross section and it is emitted or absorbed along the waveguide core. The idea can be used for experimental implementation of a laser or a coherent-perfect-absorber for photonic bound state that…
The authors of the recent paper [Phys. Rev. A 90, 032104 (2014)] claim to have established a time continuous formulation of path integration in the CS basis free from the mentioned inconsistency. Since a few recent investigations consider the approach advocated in [Phys. Rev. A 90, 032104 (2014)] as providing a "remedy" for the CS path-integral anomaly , I feel it is appropriate to show that the "recipe" proposed does not eliminate the anomaly.
We present results from a study of the coherence properties of a system involving three discrete states coupled to each other by two-photon processes via a common continuum. This tripod linkage is an extension of the standard laser-induced continuum structure (LICS) which involves two discrete states and two lasers. We show that in the tripod scheme, there exist two population trapping conditions; in some cases these conditions are easier to satisfy than the single trapping condition in two-state LICS. Depending on the pulse timing, various effects can be observed. We derive some basic propert…
Solid-state quantum coherent devices are quickly progressing. Superconducting circuits, for instance, have already been used to demonstrate prototype quantum processors comprising a few tens of quantum bits. This development also revealed that a major part of decoherence and energy loss in such devices originates from a bath of parasitic material defects. However, neither the microscopic structure of defects nor the mechanisms by which they emerge during sample fabrication are understood. Here, we present a technique to obtain information on locations of defects relative to the thin film edge …
A careful reexamination of the quantization of systems with first- and second-class constraints from the point of view of coherent-state phase-space path integration reveals several significant distinctions from more conventional treatments. Most significantly, we emphasize the importance of using path-integral measures for Lagrange multipliers which ensure that the quantum system satisfies the quantum constraint conditions. Our procedures involve no delta-functionals of the classical constraints, no need for gauge fixing of first-class constraints, no need to eliminate second-class constraint…
A discrete protocol for teleportation of superpositions of coherent states of optical cavity fields is presented. Displacement and parity operators are unconventionally used in Bell-like measurement for field states.
The discrimination of coherent states is a key task in optical communication and quantum key distribution protocols. In this work, we use a photon-number-resolving detector, the transition-edge sensor, to discriminate binary-phase-shifted coherent states at a telecom wavelength. Owing to its dynamic range and high efficiency, we achieve a bit error probability that unconditionally exceeds the standard quantum limit (SQL) by up to 7.7 dB. The improvement to the SQL persists for signals containing up to approximately seven photons on average and is achieved in a single shot (i.e. without measure…
In this paper, we examine the modification of specific nonclassical properties of the nonlinear coherent state on sphere upon perpendicular propagation through an absorptive and dispersive dielectric slab at finite temperature. For this purpose, by describing the dielectric dispersion of the slab by Lorentz model, the quadrature squeezing and the Mandel parameter are evaluated for the transmitted state. A generalization of single-mode nonlinear coherent state to the continuum-mode is considered. The degree of second-order coherence is instead calculated for a continuum nonlinear coherent state…
With the progress of optical detection technology, the classical diffraction limit raised a hundred years ago has been continuously broken through. In previous experiments within fluorescence sources, one of the techniques used is detecting auto-correlation functions. The image is reconstructed by single-photon and multi-photon detecting intensities. By taking the joint intensity of more than one single-photon detectors into consideration, the point spread function of each photon emitter can be resolved even when the distance of their central position is below the classical diffraction limit. …
The entangled "Schrodinger's cat state" of a quantum and its measurement apparatus is not a paradoxical superposition of states but is instead a non-paradoxical superposition of nonlocal coherent correlations between states: An un-decayed nucleus is correlated with a live cat, and a decayed nucleus is correlated with a dead cat. This elucidation of entanglement is demonstrated by quantum-theoretical analysis and by experiments performed in 1990 using entangled photon pairs. Thus the cat state does not predict a dead-and-alive cat. Instead of indefinite superpositions, it predicts mixtures of d…
It is shown that the maximal phase sensitivity of a two-path interferometer with high-intensity coherent light and squeezed vacuum in the input ports can be achieved by photon-number-resolving detection of only a small number of photons in a dark output port. It is then possible to achieve the quantum Cramér-Rao bound of the two-path interferometer using only the field displacement dependence of the photon number statistics in the single mode output of the dark port represented by a field-displaced squeezed vacuum state. We find that, at small field displacements, it is not sufficient to use t…
