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Register a new userFull-polaron master equation approach to dynamical steady states of a driven two-level system beyond the weak system-environment coupling
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We apply a full-polaron master equation and a weak-coupling non-Markovian master equation to describe the steady-state time-averaged properties of a driven two-level system, an electron coherently tunneling between double quantum dots (DQDs), interacting with a bosonic phonon bath. Comparing the results obtained using these two master equations with those from a recent DQD experiment and its corresponding weak-coupling theoretical method, we find that the original parameter set used in the experiment and theoretical method is not in the weak-coupling parameter regime. By using the full-polaron master equation with a slight adjustment on only the value of the interdot separation in the original experimental parameter set, we find that a reasonable fit to the experimentally measured time-averaged steady-state population data can be achieved. The adjusted interdot separation is within the possible values allowed by the geometry of the surface gates that define the DQD in the experiment. Our full-polaron equation approach does not require the special renormalization scheme employed in their weak-coupling theoretical method, and can still describe the experimental results of driving-induced phonon-enhanced steplike shoulder behaviors in the experiment. This demonstrates that the full-polaron master equation approach is a correct and efficient tool to describe the steady-state properties of a driven spin-boson model in the case of strong system-environment coupling.
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Quantum systems driven by strong oscillating fields are the source of many interesting physical phenomena. In this work, we experimentally study the dynamics of a two-level system of a single spin driven in the strong-driving regime where the rotating-wave approximation is not valid. This two-level system is a subsystem of a single Nitrogen-Vacancy center coupled to a first-shell $^{13}$C nuclear spin in diamond at a level anti-crossing point that occurs in the $m_{s}=pm1$ manifold when the energy level splitting between the $m_{s}$ = $+1$ and $-1$ spin states due to the static magnetic field is $approx$ 127 MHz, which is roughly equal to the spectral splitting due to the $^{13}$C hyperfine interaction. The transition frequency of this electron spin two-level system in a static magnetic field of 28.9 G is 1.7 MHz and it can be driven only by the $z$-component of the RF field. Electron spin Rabi frequencies in this system can reach tens of MHz even for moderate RF powers. The simple sinusoidal Rabi oscillations that occur when the amplitude of the driving field is much smaller than the transition frequency become complex when the driving field strength is comparable or greater than the energy level splitting. We observe that the system oscillates faster than the amplitude of the driving field and the response of the system shows multiple frequencies.
We present a detailed microscopic derivation for a non-Markovian master equation for a driven two-state system interacting with a general structured reservoir. The master equation is derived using the time-convolutionless projection operator technique in the limit of weak coupling between the two-state quantum system and its environment. We briefly discuss the Markov approximation, the secular approximation and their validity.
The recently developed technique combining the weak coupling limit with the Floquet formalism is applied to a model of two-level atom driven by a strong laser field and weakly coupled to heat baths. Firstly, the case of a single electromagnetic bath at zero temperature is discussed and the formula for resonance fluorescence is derived. The expression describes the well-known Mollow triplet, but its details differ from the standard ones based on additional simplifying assumptions. The second example describes the case of two thermal reservoirs: an electromagnetic one at finite temperature and the second dephasing one, which can be realized as a phononic or buffer gas reservoir. It is shown using the developed thermodynamical approach that the latter system can work in two regimes depending on the detuning sign: a heat pump transporting heat from the dephasing reservoir to an electromagnetic bath or can heat both, always at the expense of work supplied by the laser field.
For open systems described by the quantum master equation (QME), we investigate the excess entropy production under quasistatic operations between nonequilibrium steady states. The average entropy production is composed of the time integral of the instantaneous steady entropy production rate and the excess entropy production. We propose to define average entropy production rate using the average energy and particle currents, which are calculated by using the full counting statistics with QME. The excess entropy production is given by a line integral in the control parameter space and its integrand is called the Berry-Sinitsyn-Nemenman (BSN) vector. In the weakly nonequilibrium regime, we show that BSN vector is described by $ln breve{rho}_0$ and $rho_0$ where $rho_0$ is the instantaneous steady state of the QME and $breve{rho}_0$ is that of the QME which is given by reversing the sign of the Lamb shift term. If the system Hamiltonian is non-degenerate or the Lamb shift term is negligible, the excess entropy production approximately reduces to the difference between the von Neumann entropies of the system. Additionally, we point out that the expression of the entropy production obtained in the classical Markov jump process is different from our result and show that these are approximately equivalent only in the weakly nonequilibrium regime.
We study the long-time average of the reduced density matrix (RDM) of a two-level system as the central system, which is locally coupled to a generic many-body quantum chaotic system as the environment, under an overall Schr{o}dinger evolution. The system-environment interaction has a generic form with dissipation. It is shown that, in addition to the exact relations due to unit trace and hermiticity, an approximate relation exists among elements of the averaged RDM computed in the eigenbasis of the central systems Hamiltonian in some interaction regimes. In particular, an explicit expression of the relation is derived for relatively strong interactions, whose strength is above the mean level spacing of the environment, meanwhile, remains small compared with the central systems level spacing. Numerical simulations performed in a model with the environment as a defect Ising chain confirm the analytical predictions.
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