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arXiv:quant-ph/0612201 · Journal of Physics B Atomic Molecular and Optical Physics

Decoherence-induced geometric phase in a multilevel atomic system

Shubhrangshu Dasgupta, Daniel A. Lidar

Published Apr 18, 2007• 18 citations
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Abstract

We consider the STIRAP process in a three-level atom. Viewed as a closed system, no geometric phase is acquired. But in the presence of spontaneous emission and/or collisional relaxation we numerically show that a non-vanishing, purely real, geometric phase is acquired during STIRAP, whose magnitude grows with the decay rates. We speculate that rather than viewing this decoherence-induced geometric phase as a nuisance, it can be considered an example of 'beneficial decoherence': the environment provides a mechanism for the generation of geometric phases which would otherwise require an extra experimental control knob.

DOI
10.1088/0953-4075/40/9/s07

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We consider the STIRAP process in a three-level atom. Viewed as a closed system, no geometric phase is acquired. But in the presence of spontaneous emission and/or collisional relaxation we numerically show that a non-vanishing, purely real, geometric phase is acquired during STIRAP, whose magnitude grows with the decay rates. We speculate that rather than viewing this decoherence-induced geometric phase as a nuisance, it can be considered an example of 'beneficial decoherence': the environment provides a mechanism for the generation of geometric phases which would otherwise require an extra experimental control knob.
I present a feasible scheme to investigate the geometric phase for an atom trapped in an optical cavity induced by the effective decay process due to cavity-photon loss. The cavity mode, together with the external driving fields, acts as the engineered environment of the atom. When the parameters of the reservoir are adiabatically and cyclically changed, the system initially in the nontrivial dark state of the effective Lindblad operator undergoes a cyclic evolution and acquires a geometric phase. The geometric phase can be observed with the atomic-Ramsey-interference oscillation in the decoherence-free subspace.
We present a feasible scheme to investigate the geometric phase for an atom trapped in an optical cavity induced by the effective decay process due to cavity photon loss. The cavity mode, together with the external driving fields, acts as the engineered environment of the atom. When the parameters of the reservoir is adiabatically and cyclically changed, the system initially in the nontrivial dark state of the effective Lindblad operator undergoes a cyclic evolution and acquires a geometric phase. The geometric phase can be observed with the atomic Ramsey interference oscillation in the decoherence-free subspace.
We analyze the influence of three pulsed laser fields interacting with a four-state atomic system for which there occur two degenerate population-trapping dressed states. We present a simple expression for the geometrical phase acquired by such an atom during a stimulated Raman adiabatic passage (STIRAP) process using a delay between Stokes and pump pulses, during which the two Rabi frequencies adiabatically traverse a closed path in the parameter space. We describe techniques that can produce (geometrical) state-vector phases that are independent of the longitudial velocity with which atoms move across a laser beam, and that are insensitive to radiative decay from the intermediate excited state. The geometrical phase can be changed by changing the relative delay of the pulses. The geometrical phase can be measured by observing the population in atomic states. We show that when the pump and Stokes pulses are properly timed, high population transfer from the initial state to the target state is achieved. In the adiabatic limit the robustness of the population transfer is equivalent to that of STIRAP.
We study defects in adiabatic control of a quantum system caused by the entanglement of the system with its environment. Such defects can be assimilated to decoherence processes due to perturbative couplings between the system and the environment. To analyse these effects, we propose a geometric approach based on a field theory on the control manifold issued from the higher gauge theory associated with the C∗C^*C∗-geometric phases. We study a visualization method to analyse the defects of adiabatic control based on the drawing of the field strengths of the gauge theory. To illustrate the present methodology we consider the example of the atomic STIRAP (stimulated Raman adiabatic passage) where the controlled atom is entangled with another atom. We study the robustness of the STIRAP effect when the controlled atom is entangled with another one.
We investigate a scheme for an environment-induced geometric phase based on a multi-level artificial atom, initially prepared in a mixed state, that is sent through a superconducting cavity. It is shown that the environment provides a mechanism for the generation of a long-lived geometric phase. Owing to the effect of the decoherence, the solution of the master equation allows one to calculate the W-function for the multi-level system. In this regime the negativity disappears due to a stronger decoherence.
We first consider stimulated Raman adiabatic passages in a closed four-level tripod system. In this case, the adiabatic eigenstates of the system acquire real geometric phases. When the system is open and subject to decoherence they acquire complex geometric phases that we determine by a Monte Carlo wave function approach. We calculate the geometric phases and the state evolution in the closed as well as in the open system cases and describe the deviation between these in terms of the phases acquired. When the system is closed, the adiabatic evolution implements a Hadamard gate. The open system implements an imperfect gate and hence has a fidelity below unity. We express this fidelity in terms of the acquired geometric phases.