Langevin–Bloch equations for a spin bath

Abstract

We derive the Bloch equations for a two-level system coupled to a spin bath of infinitely many two-level atoms to examine phase and energy relaxation of an optically excited system. We show that increasing temperature assists coherence. This is reflected in a number of anomalous features of relaxation of the system, e.g., decrease of integrated absorption coefficient with temperature, nonlinear variation of linewidth with incident power. We also predict that thermally induced coherence may result in anomalous narrowing of linewidth, reminiscent (but distinct) of "motional narrowing" of spectral line. The theoretical results are discussed in the light of absorption-emission experiments on single quantum dots.

Controllable dynamics of a dissipative two-level system

“…One can see T −1 1 = 2T −1 2 , this relation is consistent with several previous studies [29,[49][50][51].…”

Fluctuation corrections to thermodynamic functions: Finite-size effects

“…(3.28) does not make it meaningful above the saturation temperature. This is because the system gets decoupled from the bath above this temperature [15,25,26]. This can be ascertained from the effective spectral density and by expressing 1 2 tanh ω 2KT = 1 2 − 1 e ω/KT +1 = − Ŝz where Ŝz is a measure of the population difference between the two levels of a bath atom.…”

“…To be specific, the behaviour of specific heat for small systems can be analysed by examining the finite size effects of the system [10][11][12][13]. The strategy for calculation is based on the free energy of the spin system coupled to the spin bath [14,15] minus the free energy of the spin bath in absence of the system. The desired free energy of the interacting spin system turns out to be an integral over the free energy of a single system multiplied by a density of states related to the susceptibility [16] derived explicitly from the associated c-number quantum Langevin equation.…”

“…This is the spin bath counterpart [14,15] of Wigner canonical thermal distribution function [23] for the harmonic or bosonic bath. Here N is the normalization constant.…”

Parametrically coupled fermionic oscillators: Correlation functions and phase-space description

“…However, recent experim ental advances in the field o f ferm ionic quantum atom optics [11][12][13][14][15] have opened up the possibility that the ferm ionic counterpart o f param etric am plifier could be a prom ising candidate for describing the behavior o f ferm ionic four-w ave m ixing [16], association o f ferm ionic atom s into m olecules [17][18][19], or phase sensitivity o f ferm ionic interferom eter [20]. A lthough differences leading to distinctive behavior o f a ferm ionic oscillator in contrast to a traditional harm onic oscillator have been em phasized in several earlier issues, particularly, in connection with dissipative quantum coherence [21][22][23][24], full understanding o f their im plications to other areas is rather new. Experim ental control over degenerate quantum gases o f neutral atom s in this regard sets up a new stage w here the atom ic correlations and the quantum statistics o f the constituent atom s can be directly probed by analyzing the tim e-of-flight (TOF) absorption im ages o f the atom ic gases [11][12][13][14], W hile the m ost direct analogy w ith quantum optics corresponds to the case o f bosonic statistics o f param etric dow n-conversion realized through dissociation o f a B ose-Einstein condensate (BEC) o f m olecular dim ers 23N a2 and 87R b2 [25,26], the dissociation o f 40K2 [27] The basis o f this analysis for the description o f the statistical behavior o f the two interacting ferm ionic m odes is based on a tim e-dependent density operator, w hich is well known for m ore fam iliar bosonic fields over many decades [28,29], However, the m ain reason for w hich the straightforw ard ex tension o f the schem e to their ferm ionic counterpart rem ained problem atic for a long tim e is the anticom m uting nature o f ferm ionic operators [30], To overcom e this difficulty, Cahill and G lauber have shown in their sem inal w ork on the density operator for ferm ions [31] using a practical calculus o f anti com m uting num bers that the m athem atical m ethods that have been used to analyze the statistical properties o f boson fields have their counterpart for ferm ionic fields.…”