Probing the dynamics of an open quantum system via a single qubit

Abstract

We investigate the possibility to monitor the dynamics of an open quantum system with the help of a small probe system, coupled via dephasing coupling to the open system of interest. As an example, we consider a dissipative harmonic oscillator and a single qubit as probe system. Qubit plus oscillator are described by a finite temperature quantum master equation, where the dynamics of the whole system can be obtained analytically. We find that the short time behavior of the reduced qubit state (its coherence) provides exhaustive information on the dissipative dynamics of the oscillator. Observing this coherence for two initial states with different out-of-equilibrium temperatures, one can determine all coupling constants and the equilibrium temperature fixed by the external heat bath. In addition, the dephasing coupling to the qubit probe, may be considered as a perturbation of the dissipative oscillator. The corresponding quantum fidelity can be calculated analytically, also. Hence, we find the precise relation between the behavior of the reduced qubit state (its coherence) and that fidelity.

Canonical Hamiltonian ensemble representation of dephasing dynamics and the impact of thermal fluctuations on quantum-to-classical transition

“…Our results suggest that there are discrepancies between the nonclassicality and non-Markovianity, which raise the question of the true quantum non-Markovianity 85 . Notably, as the aforementioned transition phenomenon is even manifest from the shape of CHERs, this may stimulate the development of the techniques of probe for the properties of ambient environments 86 – 90 .…”

Fast driven quantum systems: interaction picture and boundary conditions

“…In the next section, we obtain an effective equation for fast driven systems with Hamiltonian (1) in the interaction picture (in the first-order approximation in Ω −1 ). It turns out to be equivalent to (2), which serves as one more confirmation of the correctness of the derivation of such effective equations for rapidly driven systems.…”

“…As noted in [1], in quantum dynamics, even a small number of periodically-driven spins lead to complicated dynamics. The study of the dynamics of such systems (in particular, with high-frequency external influence, the so-called fast driven systems) has become an integral part of quantum physics [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. As stated in [18], the analysis of a physical problem may be simplified by taking into account the presence of substantially different characteristic scales, not only temporal, but also spatial or others.…”

Non-Markovian temperature sensing

“…Roughly speaking, there are two totally different quantum thermometers in the present existent temperature sensing schemes: the fully thermalized thermometer [4,10,11,[13][14][15][16] and the partly thermalized thermometer [6][7][8][9][17][18][19][20][21]. If the sensor-reservoir interaction is weak and the encoding time is sufficiently long, one can regard the sensor as being completely thermalized, namely, the sensor evolves to its thermal equilibrium state which is independent of the encoding time.…”

“…However, many previous studies of the partly thermalized thermometer restricted their attentions to the Born-Markov approximation [7,8,21], the weak-sensorreservoir-coupling regime [27], or the pure dephasing encoding mechanism [6,17,19]. Such treatments can provide an analytical result as well as a intuitionistic picture, but inevitably ignore certain important physical phenomena.…”