Speed of Markovian relaxation toward the ground state

Journal Article · Fri Jan 15 00:00:00 EST 2010 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.81.012102· OSTI ID:21408143

Vogl, Malte; Schaller, Gernot; Brandes, Tobias ^[1]

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1. Institut fuer Theoretische Physik, Technische Universitaet Berlin, Hardenbergstr. 36, D-10623 Berlin (Germany)

For sufficiently low reservoir temperatures, it is known that open quantum systems subject to decoherent interactions with the reservoir relax toward their ground state in the weak coupling limit. Within the framework of quantum master equations, this is formalized by the Born-Markov-secular (BMS) approximation, where one obtains the system Gibbs state with the reservoir temperature as a stationary state. When the solution to some problem is encoded in the (isolated) ground state of a system Hamiltonian, decoherence can therefore be exploited for computation. The computational complexity is then given by the scaling of the relaxation time with the system size n. We study the relaxation behavior for local and nonlocal Hamiltonians that are coupled dissipatively with local and nonlocal operators to a bosonic bath in thermal equilibrium. We find that relaxation is generally more efficient when coherences of the density matrix in the system energy eigenbasis are taken into account. In addition, the relaxation speed strongly depends on the matrix elements of the coupling operators between initial state and ground state. We show that Dicke superradiance is a special case of our relaxation models and can thus be understood as a coherence-assisted relaxation speedup.

• OSTI ID: 21408143
• Journal Information: Physical Review. A, Vol. 81, Issue 1; Other Information: DOI: 10.1103/PhysRevA.81.012102; (c) 2010 The American Physical Society; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COUPLING
DENSITY MATRIX
GROUND STATES
HAMILTONIANS
MARKOV PROCESS
MATHEMATICAL SOLUTIONS
MATRIX ELEMENTS
RELAXATION
RELAXATION TIME
RESERVOIR TEMPERATURE
SUPERRADIANCE
THERMAL EQUILIBRIUM
VELOCITY
EMISSION
ENERGY LEVELS
ENERGY-LEVEL TRANSITIONS
EQUILIBRIUM
MATHEMATICAL OPERATORS
MATRICES
PHOTON EMISSION
QUANTUM OPERATORS
STIMULATED EMISSION
STOCHASTIC PROCESSES