Temperature-enhanced squeezing in cavity QED

Spehner, Dominique; Orszag, Miguel

doi:10.1088/1464-4266/4/5/315

Cited by 1 publication

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“…Second, X t is interpreted as the evolution of the state of a quantum system conditioned on continuous measurement (see, e.g., [4,8,19,30,51,59]). For instance, the following example describes the simultaneous monitoring of position and momentum of a quantum system whose evolution is governed by the Hamiltonian H (see, e.g., [32,57]).…”

Section: Nonlinear Stochastic Schr öDinger Equationsmentioning

confidence: 99%

“…On the other hand, the value of the observable A at time t T t (A) satisfies E X t , AX t = E X 0 , T t (A)X 0 (see, e.g., [3,34,35]). Recall that quantum observables are represented by self-adjoint operators in h.Second, X t is interpreted as the evolution of the state of a quantum system conditioned on continuous measurement (see, e.g., [4,8,19,30,51,59]). For instance, the following example describes the simultaneous monitoring of position and momentum of a quantum system whose evolution is governed by the Hamiltonian H (see, e.g., [32,57]).…”

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Basic properties of nonlinear stochastic Schrödinger equations driven by Brownian motions

Mora¹,

Rebolledo²

2008

Ann. Appl. Probab.

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The paper is devoted to the study of nonlinear stochastic Schrödinger equations driven by standard cylindrical Brownian motions (NSSEs) arising from the unraveling of quantum master equations. Under the Born-Markov approximations, this class of stochastic evolutions equations on Hilbert spaces provides characterizations of both continuous quantum measurement processes and the evolution of quantum systems. First, we deal with the existence and uniqueness of regular solutions to NSSEs. Second, we provide two general criteria for the existence of regular invariant measures for NSSEs. We apply our results to a forced and damped quantum oscillator. . This reprint differs from the original in pagination and typographic detail. 1The interaction of the small system with the reservoir is simulated by L 1 = α 1 a, L 2 = α 2 a † , L 3 = α 3 N , L 4 = α 4 a 2 , L 5 = α 5 (a † ) 2 , and L 6 = α 6 N 2 , where β 1 , β 2 , β 3 are real numbers and α 1 , . . . , α 6 are complex numbers. Consider L k = 0 for all k ≥ 7. NONLINEAR STOCHASTIC SCHRÖDINGER EQUATIONS 3In Example 1, h represents the state space of a single mode of a quantized electromagnetic field and the vectors e n , with n ∈ Z + , provide the energy levels of the system. Because a destroys a photon, L 1 , L 4 model photon emissions. The operator a † describes the creation of a photon (see, e.g., [16,56]).Using (1), we can obtain a probabilistic representation of ρ t . Indeed, it is to be expected that ρ t = E|X t X t | (see, e.g., [6,31,51]). In Dirac notation, |x x|, with x ∈ h, stands for the linear operator defined by |x x|(z) = x, z x for any z ∈ h. Therefore, the probability that a measurement finds the system in the pure state x at time t ≥ 0 is E| x, X t | 2 assuming that E|X 0 X 0 | is the initial density operator and x is a vector of h of norm 1. On the other hand, the value of the observable A at time t T t (A) satisfies E X t , AX t = E X 0 , T t (A)X 0 (see, e.g., [3,34,35]). Recall that quantum observables are represented by self-adjoint operators in h.Second, X t is interpreted as the evolution of the state of a quantum system conditioned on continuous measurement (see, e.g., [4,8,19,30,51,59]). For instance, the following example describes the simultaneous monitoring of position and momentum of a quantum system whose evolution is governed by the Hamiltonian H (see, e.g., [32,57]).

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