Abstract
We describe an efficient numerical method for simulating the dynamics and steady states of collective spin systems in the presence of dephasing and decay. The method is based on the Schwinger boson representation of spin operators and uses an extension of the truncated Wigner approximation to map the exact open system dynamics onto stochastic differential equations for the corresponding phase space distribution. This approach is most effective in the limit of very large spin quantum numbers, where exact numerical simulations and other approximation methods are no longer applicable. We benchmark this numerical technique for known superradiant decay and spin-squeezing processes and illustrate its application for the simulation of non-equilibrium phase transitions in dissipative spin lattice models.
Highlights
Large ensembles of two-level systems that can be approximately modeled as a single collective spin are of interest in many areas of physics
The coupling of large ensembles of two-level systems to a common environment can lead to new physical phenomena, such as phase-locked condensates in equilibrium [8], or superradiant [1, 9] and super-correlated [10] decay
For weakly interacting bosonic systems such phase space methods based on the truncated Wigner approximation (TWA) are well established and can be used, for example, to simulate dissipative bosonic lattice systems and non-equilibrium condensation phenomena [23–27]
Summary
Large ensembles of two-level systems that can be approximately modeled as a single collective spin are of interest in many areas of physics. For weakly interacting bosonic systems such phase space methods based on the TWA are well established and can be used, for example, to simulate dissipative bosonic lattice systems and non-equilibrium condensation phenomena [23–27] The extension of these methods to spin systems via the Schwinger representation has previously been applied for simulating the coherent dynamics of lattices of spin-1/2 systems [28, 29] and that of collective spins [22]. As a result of this approximation, the stochastic equations in phase space are well-behaved for arbitrary times, which allows us to evaluate the long-time dynamics and the steady states of dissipative spin systems that have been inaccessible so far Using this truncated Wigner method for open quantum spins (TWOQS), we obtain an approximately linear scaling with the number of collective spins included, in any dimension and for arbitrary interaction patterns.
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