Quantum energy and coherence exchange with discrete baths

Abstract

h i g h l i g h t s• Quantum coherence of systems coupled to finite baths composed of N harmonic oscillators is investigated. • A stochastic Schrödinger equation is solved numerically. • The energy and purity exchange between system and bath are described in details as a function of the numbers of bath harmonic oscillators.• The non-Markovian dynamics due to finite baths is analyzed. a b s t r a c tCoherence and quantum average energy exchange are studied for a system particle as a function of the number N of constituents of a discrete bath model. The time evolution of the energy and coherence, determined via the system purity (proportional to the linear entropy of the quantum statistical ensemble), are obtained solving numerically the Schrödinger equation. A new simplified stochastic Schrödinger equation is derived which takes into account the discreteness of the bath. The environment (bath) is composed of a finite number N of uncoupled harmonic oscillators (HOs), characterizing a structured bath, for which a non-Markovian behavior is expected. Two distinct physical situations are assumed for the system particle: the HO and the Morse potential. In the limit N → ∞ the bath is assumed to have an ohmic, sub-ohmic or super-ohmic spectral density. In the case of the HO, for very low values of N ( 10) the mean energy and purity oscillate between HO and bath indefinitely in time, while for intermediate and larger values (N ∼ 10 → 500) they start to decay with two distinct time regimes: exponential for relatively short times and powerlaw for larger times. In the case of the Morse potential we only observe an exponential decay for large values of N while for small N's, due to the anharmonicity of the potential, no recurrences of the mean energy and coherences are observed. Wave packet dynamics is used to determine the evolution of the particle inside the system potentials. For both systems the time behavior of a non-Markovianity measure is analyzed as a function of N and is shown to be directly related to the time behavior of the purity.

Toppling Pencils—Macroscopic Randomness from Microscopic Fluctuations

“…In this point, however, we adopt a more recent development in statistical mechanics, in that we keep the number of oscillators large, , but finite [ 8 , 9 , 10 , 11 , 12 ], so that the dynamics of the total system can be treated in the framework of the time-reversal invariant Hamiltonian mechanics of closed systems. It has been demonstrated for classical as well as for quantum systems [ 13 , 14 ], and is corroborated by the present work, that despite its time-reversal symmetry, this approach reproduces irreversible behaviour on all relevant timescales. Poincaré recurrences, which prevent true irreversibility in systems with a finite number of freedoms, occur only on timescales that diverge geometrically with N [ 15 ].…”

Quantum Chaos and Quantum Randomness—Paradigms of Entropy Production on the Smallest Scales

“…This price appears acceptable, though, as long as a faithful description of the processes of interest is required only over a correspondingly large, but finite time scale, as is the case, for example, in computational molecular physics and in quantum optics. Numerical experiments simulating decoherence with heat baths of finite Hilbert space dimension [ 79 , 80 , 81 ] provide convincing evidence that even with a surprisingly low number of bath modes, N of the order of 10, most relevant features of decoherence can be satisfactorily reproduced; see Figure 16 . This suggests to restrict the dimension of the meter sector of the Hilbert space underlying the Hamiltonian ( 58 ) accordingly to a finite number N , Like this, the Hamiltonian can be considered as a model of, e.g., a two-level atom in a high- Q microwave cavity [ 76 ].…”

“…Experience with similar models comprising finite baths [ 79 , 81 ], suggests the following scenario: For small values , the time evolution comprises only a few, but typically incommensurate, frequencies and should appear quasi-periodic. Already for moderate numbers, say , the unitary model will exhibit a similar behavior as has been observed for standard models of quantum optics and solid-state physics, known as “collapses and revivals” [ 76 ].…”

“…( d ) Degree of memory, measured as the non-Markovianity , denoting the purity as depicted in panel ( b ). Reproduced from [ 81 ] with kind permission.…”

Environment-induced quantum coherence spreading of a qubit

“…This process is normally accompanied by the loss of the system's QC, which is induced by the spontaneous creation of correlations between it and its surroundings. It is worthwhile mentioning that similar issues have been investigated previously, but mainly with regard to decorrelating dynamics for composite systems interacting with local or global environments, or in the thermodynamical, non-Markovianity, and sensing contexts [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47]. The goal of the present contribution is to provide a thorough description of the dynamical flow of a quantum coherence monotone, the l 1 -norm QC, during the time evolution of a qubit interacting with environments modeled by quantum channels important for quantum information science [48][49][50].…”