Born-Oppenheimer approximation for open quantum systems within the quantum trajectory approach

Huang, Xiao-Li; Wu, Shunan; Wang, L. C.

doi:10.1103/physreva.81.052113

Phys. Rev. A

2010

DOI: 10.1103/physreva.81.052113

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Born-Oppenheimer approximation for open quantum systems within the quantum trajectory approach

Xiao-Li Huang

Shunan Wu

L. C. Wang

Abstract: Using the quantum trajectory approach, we extend the Born-Oppenheimer (BO) approximation from closed to open quantum systems, where the open quantum system is described by a master equation in Lindblad form. The BO approximation is defined and the validity condition is derived. We find that the dissipation in fast variables improves the BO approximation, unlike the dissipation in slow variables. A detailed comparison is presented between this extension and our previous approximation based on the effective Hami… Show more

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2012

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Cited by 2 publications

References 43 publications

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Adiabatic and nonadiabatic contributions to the energy of a system subject to a time-dependent perturbation: Complete separation and physical interpretation

Mandal

Hunt

2012

The Journal of Chemical Physics

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When a time-dependent perturbation acts on a quantum system that is initially in the nondegenerate ground state ∣0> of an unperturbed Hamiltonian H(0), the wave function acquires excited-state components ∣k> with coefficients c(k)(t) exp(-iE(k)t/ℏ), where E(k) denotes the energy of the unperturbed state ∣k>. It is well known that each coefficient c(k)(t) separates into an adiabatic term a(k)(t) that reflects the adjustment of the ground state to the perturbation--without actual transitions--and a nonadiabatic term b(k)(t) that yields the probability amplitude for a transition to the excited state. In this work, we prove that the energy at any time t also separates completely into adiabatic and nonadiabatic components, after accounting for the secular and normalization terms that appear in the solution of the time-dependent Schrödinger equation via Dirac's method of variation of constants. This result is derived explicitly through third order in the perturbation. We prove that the cross-terms between the adiabatic and nonadiabatic parts of c(k)(t) vanish, when the energy at time t is determined as an expectation value. The adiabatic term in the energy is identical to the total energy obtained from static perturbation theory, for a system exposed to the instantaneous perturbation λH'(t). The nonadiabatic term is a sum over excited states ∣k> of the transition probability multiplied by the transition energy. By evaluating the probabilities of transition to the excited eigenstates ∣k'(t)> of the instantaneous Hamiltonian H(t), we provide a physically transparent explanation of the result for E(t). To lowest order in the perturbation parameter λ, the probability of finding the system in state ∣k'(t)> is given by λ(2) ∣b(k)(t)∣(2). At third order, the transition probability depends on a second-order transition coefficient, derived in this work. We indicate expected differences between the results for transition probabilities obtained from this work and from Fermi's golden rule.

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Adiabatic and nonadiabatic contributions to the energy of a system subject to a time-dependent perturbation: Complete separation and physical interpretation

Mandal

Hunt

2012

The Journal of Chemical Physics

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Entanglement of distant optomechanical systems

et al. 2012

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We theoretically investigate the possibility to generate non-classical states of optical and mechanical modes of optical cavities, distant from each other. A setup comprised of two identical cavities, each with one fixed and one movable mirror and coupled by an optical fiber, is studied in detail. We show that with such a setup there is potential to generate entanglement between the distant cavities, involving both optical and mechanical modes. The scheme is robust with respect to dissipation, and nonlocal correlations are found to exist in the steady state at finite temperatures.

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Born-Oppenheimer approximation for open quantum systems within the quantum trajectory approach

Cited by 2 publications

References 43 publications

Adiabatic and nonadiabatic contributions to the energy of a system subject to a time-dependent perturbation: Complete separation and physical interpretation

Adiabatic and nonadiabatic contributions to the energy of a system subject to a time-dependent perturbation: Complete separation and physical interpretation

Entanglement of distant optomechanical systems

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