Superposed photon-added and photon-subtracted squeezed-vacuum states exhibit sub-Planck phase-space structures and metrological potential similar to the original compass states (superposition of four coherent states), but are more closely tied to modern experiments. Here, we observe that these compasslike states are highly susceptible to loss of quantum coherence when placed in contact with a thermal reservoir; that is, the interaction with the thermal reservoir causes decoherence, which progressively suppresses the capacity of these states to exhibit interference traits. We focus on the sub-Planck structures of these states and find that decoherence effects on these features are stronger with increasing the average thermal photon number of the reservoir, the squeezing parameter, or the quantity of added (or subtracted) photons to the squeezed-vacuum states. Furthermore, we observe that the sub-Planck structures of the photon-subtracted case survive comparatively longer in the thermal reservoir than their counterparts in the photon-added case, and prolonged contact with the thermal reservoir converts these compasslike states into a classical state.
The Wigner function of the compass state (a superposition of four coherent states) develops phase-space structures of dimension much less than the Planck scale $\ensuremath{\hbar}$, which are crucial in determining the sensitivity of these states to phase-space displacements. In the present work we introduce compasslike states that may have connection to the contemporary experiments, which are obtained by either adding photons to or subtracting photons from the superposition of two squeezed-vacuum states. We show that when a significant quantity of photons is added (or subtracted), the Wigner functions of these states are shown to have phase-space structures of an area that is substantially smaller than the Planck scale. In addition, these states exhibit sensitivity to displacements that is much higher than the standard quantum limit. Finally, we show that both the size of the sub-Planck structures and the sensitivity of our states are strongly influenced by the average photon number, with the photon-addition case having a higher average photon number leading to the smaller sub-Planck structures and, consequently, being more sensitive to displacement than the photon-subtraction case. Our states offer unprecedented resolution to the external perturbations, making them suitable for quantum sensing applications.
Environmental decoherence occurs when a quantum system interacts with its surroundings, progressively reducing quantum interference and coherence, complicating the preservation of critical quantum features over time, especially during experimental implementation. The quantum features of a state can be represented in phase space via the Wigner function, which manifests across multiple scales, with decoherence potentially influencing each scale differently, as examined in this work. We consider the compass state and its photon-added and photon-subtracted variants (optimized compass states) as our representative examples, each of which exhibits phase-space features with dimensions beyond the Planck scale, making them suitable for quantum sensing applications. We investigate the interaction of these states with a heat reservoir by employing a range of well-established theoretical tools. We observe that compass states with finer-scale phase-space features are more fragile to decoherence, with parameters favoring greater sub-Planckness in phase space concomitantly increasing the fragility of these compass states to decoherence. Our findings are then validated for generic quantum states interacting with the heat reservoir, for which we provide analytical and numerical investigations, exploring the relationship between quantum state robustness to decoherence and the sizes of their phase-space features; that is, phase-space features at smaller scales decay faster under decoherence, and vice versa.
We discuss the nonclassical properties of photon subtracted compass states (PSCS). Nonclassical behavior is studied using various parameters like the Wigner function, squeezing, and photon statistical parameters like Mandels Q function, secondorder correlation function, Agarwal Tara
A3 criterion, and photon number distribution. Further analysis is being done to investigate the subPlanck structures in the Wigner functions of these PSCS. We also show that the photon subtraction causes the loss of sensitivity due to displacement of the states in phase space.
Quantum states with sub-Planck features exhibit sensitivity to phase-space displacements beyond the standard quantum limit, making them useful for quantum metrology. In the context of the SU(1,1) group, sub-Planck features have been constructed through the superposition of four Perelomov coherent states on the hyperbolic plane (the SU(1,1) compass state). However, these structures differ in scale along different phase-space directions (anisotropic features), resulting in nonuniform sensitivity enhancement to phase-space displacements. Here, we construct
N-component compass states, which are obtained by superposing
N≥6 SU(1,1) coherent states with an even total number, evenly arranged along a circular path on the hyperbolic plane; that is, all components lie at the same distance from the origin and have equal angular spacing of
N2π. We observe that these generalized SU(1,1) compass states exhibit isotropic sub-Planck structures, leading to an isotropic enhancement in sensitivity to phase-space displacements that progressively increases with larger
N. These states are directly relevant to quantum platforms supporting Kerr-type interactions between two bosonic modes, where the underlying SU(1,1) dynamical symmetry enables the generation of multicomponent SU(1,1) compass states. Specifically, the compact evolution of SU(1,1) coherent states under the considered dynamics enables the generation of multicomponent SU(1,1) compass states at specific times. We also investigate the effects of thermal decoherence on these multicomponent compass states within a frequency-resolved Lindblad framework, demonstrating the evolution and degradation of their nonclassical signatures.
We investigate nonclassicality and decoherence of field states generated with the non-Gaussian operation of photon addition to a two-mode squeezed thermal state (TSTS) using the normally ordered density operator of the photon-added TSTS (PTSTS). The normalization factor of the PTSTS is just a Jacobi polynomial of the squeezing parameter γ and the average photon number n¯ of the thermal field. We show that the fields in such states exhibit remarkable quantum features, such as sub-Poissonian photon statistics, the anti-bunching effect, and photon-number distribution. The nonclassicality is discussed in phase space based on the partial negativity of the Wigner function (WF) with two-variable Hermite polynomials. The results show that the non-Gaussian WF always exhibits the quantum interference structure caused by the two-mode squeezing operation and has some negative regions for any value of n¯, γ, and the photon-addition numbers m, n. In addition, the effect of decoherence on the PTSTS in the thermal channel is studied by analytically deriving the time-evolution WF. We find that the WF becomes Gaussian (corresponding to a classical thermal state) at long times, losing its nonclassicality as a result of decoherence, and a larger m (or n) leads to a longer decoherence time κt.
We discuss nonclassical properties of single-photon subtracted squeezed vacuum states in terms of the sub-Poissonian statistics and the negativity of the Wigner function. We derive a compact expression for the Wigner function from which we find the region of phase space where Wigner function is negative. We find an upper bound on the squeezing parameter for the state to exhibit sub-Poissonian statistics. We then study the effect of decoherence on the single-photon subtracted squeezed states. We present results for two different models of decoherence, viz. amplitude decay model and the phase diffusion model. In each case we give analytical results for the time evolution of the state. We discuss the loss of nonclassicality as a result of decoherence. We show through the study of their phase-space properties how these states decay to vacuum due to the decay of photons. We show that phase damping leads to very slow decoherence, slower than the photon-number decay.