Quasiprobability currents on the sphere

Abstract

We present analytic expressions for the s-parametrized currents on the sphere for both unitary and dissipative evolutions. We examine the spatial distribution of the flow generated by these currents for quadratic Hamiltonians. The results are applied for the study of the quantum dissipative dynamics of the time-honored Kerr and Lipkin models, exploring the appearance of the semiclassical limit in stable, unstable and tunnelling regimes.

Experimental Demonstration of Topological Charge Protection in Wigner Current

“…Theoretical studies have confirmed that such behaviors are expected to occur in a large variety of systems such as anharmonic [16] and tunneling systems [5,19], in systems described by effectively non-Hermitian parity-time symmetric hamiltonians [20] and even in discrete (spin) systems [17,18].…”

“…But in contrast to the classical case, in the quantum case J can have stagnation points any-where in phase space, even when the momentum p = 0. These stagnation points do typically move under the dynamics whilst carrying a conserved topological charge which governs their splittings and mergers with other stagnation points [5,17,18].…”

Observation of robust polarization squeezing via the Kerr nonlinearity in an optical fibre

“…The two light fields are analyzed using the SU(2) description [66] and visualizing this system of two modes on the Poincaré sphere [67]. There is an interesting dynamics of the Wigner function on the sphere as a result of the Kerr interaction [68], [69]. Note, that measuring the Stokes parameters spanning the Poincaré sphere again involves interference and it can be done with direct detection without any additional local oscillator.…”

New phase space formulations and quantum dynamics approaches

“…Further developments of Stratonovich's formulation have focused on an SU (2) or SU(F) structure of phase space [103][104][105][106][107][108][109][110][111][112][113][114][115][116][117] , while those on the construction of a discrete phase space are described in References 78,[118][119][120][121][122][123][124][125][126] . Other than the 2-state (or spin 1/2) system, the exact equations of motion (EOMs) of phase variables (expressed by the Moyal-like bracket) involved in these approaches for the finite discrete multi-state system are often tedious and numerically unfavourable 109,[127][128][129][130][131][132] . (See Appendix 3 of the Supporting Information for more discussion.)…”

“…Further developments of Stratonovich's formulation have focused on an SU (2) or SU(F) structure of phase space, [103][104][105][106][107][108][109][110][111][112][113][114][115][116][117] while those on the construction of a discrete phase space are described in References 78,[118][119][120][121][122][123][124][125][126] Other than the 2-state (or spin 1/2) system, the exact equations of motion (EOMs) of phase variables (expressed by the Moyal-like bracket) involved in these approaches for the finite discrete multi-state system are often tedious and numerically unfavourable. 109,[127][128][129][130]299,302 (See Appendix 3 of the Supporting Information for more discussion.) Recent theoretical progress on exactly mapping the finite discrete F-state quantum system onto constraint coordinate-momentum phase space suggests that there exists a novel unified framework to derive comprehensive exact mapping Hamiltonians, 44,57,131,132 of which the quantum EOMs of mapping coordinatemomentum variables are simply linear.…”