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arXiv:quant-ph/0507101 · Physical Review Letters

Geometric Phase Induced by a Cyclically Evolving Squeezed Vacuum Reservoir

Angelo C. M. Carollo, G. Massimo Palma, Artur Łoziński, Marcelo França Santos, Vlatko Vedral

Published Apr 21, 2006• 47 citations
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Abstract

We propose a new way to generate an observable geometric phase by means of a completely incoherent phenomenon. We show how to imprint a geometric phase to a system by adiabatically manipulating the environment with which it interacts. As a specific scheme, we analyze a multilevel atom interacting with a broadband squeezed vacuum bosonic bath. As the squeezing parameters are smoothly changed in time along a closed loop, the ground state of the system acquires a geometric phase. We also propose a scheme to measure such a geometric phase by means of a suitable polarization detection.

DOI
10.1103/physrevlett.96.150403

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We propose a new way to generate an observable geometric phase by means of a completely incoherent phenomenon. We show how to imprint a geometric phase to a system by adiabatically manipulating the environment with which it interacts. As a specific scheme, we analyze a multilevel atom interacting with a broadband squeezed vacuum bosonic bath. As the squeezing parameters are smoothly changed in time along a closed loop, the ground state of the system acquires a geometric phase. We also propose a scheme to measure such a geometric phase by means of a suitable polarization detection.
In [1], a new way to generate an observable geometric phase on a quantum system by means of a completely incoherent phenomenon has been proposed. The basic idea is to force the ground state of the system to evolve cyclically by “adiabatically” manipulating the environment with which it interacts. The specific scheme analyzed in [1], consisting of a multilevel atom interacting with a broadband squeezed vacuum bosonic bath whose squeezing parameters are smoothly changed in time along a closed loop, is here solved in a more direct way. This new solution emphasizes how the geometric phase at the ground state of the system is indeed due to a purely incoherent dynamics.
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.
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.
Geometric phase, for a two-level atom in an electromagnetic field interacting with a squeezed-vacuum reservoir, is calculated by establishing connecting density matrices, describing an evolution of a quantum open system, with a nonunit vector ray in a complex projective Hilbert space. Because the geometric phase depends only on the smooth curve on this space, it is formulated entirely in terms of geometric structures. The results show that the geometric phase for the squeezed-vacuum reservoir has fully different behavior in comparison with one for the normal vacuum reservoir.
Since a pioneer work on vacuum-induced Berry phase (VIBP) was done by Fuentes-Guridi et al. [Phys. Rev. Lett. 89 (2002) 220404], much attention has been paid to the geometric phase effects of vacuum field. However, all the so-called VIBPs investigated previously are not purely vacuum-induced (i.e. the nonvacuum components of the field are also involved). In this paper, we discuss how to deliver geometric phases from the evolution of a genuine vacuum field in a standard cavity quantum electrodynamics (QED) system. First, we design a cyclic evolution of an atom–field system with the atom being initially prepared at the excited state and the field at the genuine vacuum. Then, we calculate the geometric phases acquired during such a cyclic evolution. It is found that such geometric phases are really induced by an evolution of the genuine vacuum field. Specifically, our generic proposal is demonstrated with both the one- and two-mode Jaynes–Cummings model interactions (JCM).