We consider an adiabatic Landau-Zener model of a two-level system diagonally coupled to an Ohmic bosonic bath of large spectral width and, through fermionization, derive its exact solution at a special value of the coupling constant. From this solution we obtain the characteristic function of the distribution of energy transferred to the bath during the evolution of the system ground state as a functional determinant of a single-particle operator. At zero temperature this distribution is further found to be exponential, and at finite temperature the first three moments of the distribution are calculated.
We study Landau-Zener transitions in a qubit coupled to a bath at zero temperature. A general formula that is applicable to models with a nondegenerate ground state is derived. We calculate exact transition probabilities for a qubit coupled to either a bosonic or a spin bath. The nature of the baths and the qubit-bath coupling is reflected in the transition probabilities. For diagonal coupling, when the bath causes energy fluctuations of the diabatic qubit states but no transitions between them, the transition probability coincides with the standard Landau-Zener probability of an isolated qubit. This result is universal as it does not depend on the specific type of bath. For pure off-diagonal coupling, by contrast, the tunneling probability is sensitive to the coupling strength. We discuss the relevance of our results for experiments on molecular nanomagnets, in circuit QED, and for the fast-pulse readout of superconducting phase qubits.
We calculate the exact Landau-Zener transition probabilities for a qubit with an arbitrary linear coupling to a bath at zero temperature. The final quantum state exhibits a peculiar entanglement between the qubit and the bath. In the special case of diagonal coupling, the bath does not influence the transition probability, whatever the speed of the Landau-Zener sweep. It is proposed to use Landau-Zener transitions to determine both the reorganization energy and the integrated spectral density of the bath. Possible applications include circuit QED and molecular nanomagnets.
We study Landau-Zener transitions in a fermionic dissipative environment where a two-level (up and down states) system is coupled to two metallic leads kept with different chemical potentials at zero temperature. The dynamics of the system is simulated by an iterative numerically exact influence functional path integral method. In the pure Landau-Zener problem, two kinds of transition (from up to down state and from down to up state) probability are symmetric. However, this symmetry is destroyed by coupling the system to the bath. In addition, in both kinds of transitions, there exists a nonmonotonic dependence of the transition probability on the sweep velocity; meanwhile nonmonotonic dependence of the transition probability on the system-bath coupling strength is only shown in one of them. As in the spin-boson model, these phenomena can be explained by a simple phenomenological model.
The evolution of a quantum system towards thermal equilibrium is usually studied by approximate methods, which have their limits of validity and should be checked against analytically solvable models. In this paper, we propose an analytically solvable model to investigate the energy transfer between a bosonic bath and a fermionic chain which are nonlinearly coupled to each other. The bosonic bath consists of an infinite collection of noninteracting bosonic modes, while the fermionic chain is represented by a chain of interacting fermions with nearest-neighbor interactions. We compare the behaviors of the temperature-dependent energy current
JT and temperature-independent energy current
JTI for different bath configurations. With respect to the bath spectrum,
JT decays exponentially for a Lorentz-Drude-type bath, which is the same as the conventional approximations. On the other hand, the decay rate is
1/t3 for the Ohmic type and
1/t for white noise, which does not have conventional counterparts. For the temperature-independent current
JTI, the decay rate is divergent for the Lorentz-Drude-type bath,
1/t4 for the Ohmic bath, and
1/t for the white noise. When further considering the dynamics of the fermionic chain, the current will be modulated based on the envelope from the bath. As an example, for a bosonic bath with an Ohmic spectrum, when the fermionic chain is uniformly coupled, we have ${J}_{T}\ensuremath{\propto}1/{t}^{6}$ and ${J}_{TI}\ensuremath{\propto}1/{t}^{3}$. Moreover, it is interesting that
JT is proportional to ${(N\ensuremath{-}1)}^{1/2}$ at certain times for perfect state transfer couplings under a Lorentz-Drude or Ohmic bath.
We present statistics of quantum jumps in the two-level system with landau-Zener Hamiltonian that undergoes a Markovian process. For the Landau-Zener model, which is successful in simulating adiabatic/non-adiabatic evolution and quantum annealing, we consider two types of dissipation. In the first one, the jump operators project states to the initial ground state and excited state of the Hamiltonian at
t→−∞. In the second type, the jump operators project to the instantaneous eigenstates of the Hamiltonian. By the quantum trajectories approach, we present the probability of the number of jumps in adiabatic and non-adiabatic regimes for both models. Furthermore, we demonstrate the statistics of jumps in time intervals of the evolutions. Also, we show the role of bath temperature, coupling strength to the environment, and spin-coupling directions on the statistics of quantum jumps.