Abstract
Recent advances illustrate the power of reservoir engineering in applications to many-body systems, such as quantum simulators based on superconducting circuits. We present a framework based on kinetic equations and noise spectra that can be used to understand both the transient and long-time behavior of many particles coupled to an engineered reservoir in a number-conserving way. For the example of a bosonic array, we show that the non-equilibrium steady state can be expressed, in a wide parameter regime, in terms of a modified Bose-Einstein distribution with an energy-dependent temperature.
Highlights
Reservoir engineering [1,2,3] is used to deliberately generate some desired dissipative dynamics, as demonstrated in a variety of platforms: atoms [4], superconducting circuits [5,6,7], ion traps [8,9,10], and optomechanics [11,12]
Reservoir engineering contributes to the implementation of quantum simulators, especially in cases where the naturally available dissipation would not drive the system to the right many-body ground state
By expanding on both sides of the equality and noting that the expression on the right-hand side is an odd function of ω (S(ω) is an asymmetric function of ω [27]), we find that the effective inverse temperature for a single transition frequency can be expressed as βeff (ω) = n=0 β2nω2n
Summary
Reservoir engineering [1,2,3] is used to deliberately generate some desired dissipative dynamics, as demonstrated in a variety of platforms: atoms [4], superconducting circuits [5,6,7], ion traps [8,9,10], and optomechanics [11,12]. We derive the steady state of a 1D array of bosonic modes with nearest-neighbor hopping coupled to a particle-conserving nonequilibrium reservoir. This turns out to be a “deformed” Bose-Einstein distribution with an energydependent effective temperature. Where D(ωk) denotes the density of states, is useful to find perturbative solutions describing the steady state of the system To understand how this can be done, we start by recalling that even for a noise source that is not in thermal equilibrium one can always define an effective temperature associated to a single transition frequency by using the Stokes relation S(ω)/S(−ω) = exp[βeff ω] or, alternatively, tanh[βeff ω/2] = [S(ω) − S(−ω)]/[S(ω) + S(−ω)] [27]. In other words the steady-state distribution can be understood as a certain deformed version of the Bose-Einstein distribution
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