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Laser Physics

The geometric phase in a multi-level superconducting artificial atom

Mahmoud Abdel‐Aty

Published Apr 3, 2013• 1 citation
Publisher

Abstract

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.

DOI
10.1088/1054-660x/23/5/055202

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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 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.
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 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.
We propose a relaxation rate or dissipative cavity-based parameters that can be used as indicators of the stationary limit of a mixed state geometric phase. We perform our considerations for the system of a superconducting qubit in an open transmission line or interacting with a dissipative cavity. This system is very useful for performing an effective quantum computation by exhibiting the long collapse time of the geometric phase. It is shown that the geometric phase in the stationary limit does not depend on interaction time if the decay time exceeds an upper bound.
Berry's geometric phase naturally appears when a quantum system is driven by an external field whose parameters are slowly and cyclically changed. A variation in the coupling between the system and the external field can also give rise to a geometric phase, even when the field is in the vacuum state or any other Fock state. We demonstrate the appearance of a vacuum-induced Berry phase in an artificial atom, a superconducting transmon, interacting with a single mode of a microwave cavity. As we vary the phase of the interaction, the artificial atom acquires a geometric phase determined by the path traced out in the combined Hilbert space of the atom and the quantum field. Our ability to control this phase opens new possibilities for the geometric manipulation of atom-cavity systems also in the context of quantum information processing.