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Register a new userThe Landau-Zener Model with Decoherence: The case S=1/2
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We study the dynamics of a spin coupled to an oscillating magnetic field, in the presence of decoherence and dissipation. In this context we solve the master equation for the Landau-Zener problem, both in the unitary and in the irreversible case. We show that a single spin can be magnetized in the direction parallel to the oscillating bias. When decay from upper to lower level is taken into account, hysteretic behavior is obtained.
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Two aspects of the classic two-level Landau--Zener (LZ) problem are considered. First, we address the LZ problem when one or both levels decay, i.e., $veps_j(t) to veps_j(t)-i Gamma_j/2$. We find that if the system evolves from an initial time $-T$ to a final time $+T$ such that $|veps_1(pm T)-veps_2(pm T)|$ is not too large, the LZ survival probability of a state $| j ra$ can {em increase} with increasing decay rate of the other state $|i e j ra$. This surprising result occurs because the decay results in crossing of the two eigenvalues of the instantaneous non-Hermitian Hamiltonian. On the other hand, if $|veps_1(pm T)-veps_2(pm T)| to infty$ as $T to infty$, the probability is {em independent} of the decay rate. These results are based on analytic solutions of the time-dependent Schrodinger equations for two cases: (a) the energy levels depend linearly on time, and (b) the energy levels are bounded and of the form $veps_{1,2}(t) = pm veps tanh (t/{cal T})$. Second, we study LZ transitions affected by dephasing by formulating the Landau--Zener problem with noise in terms of a Schr{o}dinger-Langevin stochastic coupled set of differential equations. The LZ survival probability then becomes a random variable whose probability distribution is shown to behave very differently for long and short dephasing times. We also discuss the combined effects of decay and dephasing on the LZ probability.
Landau-Zener physics is often exploited to generate quantum logic gates and to perform state initialization and readout. The quality of these operations can be degraded by noise fluctuations in the energy gap at the avoided crossing. We leverage a recently discovered correspondence between qubit evolution and space curves in three dimensions to design noise-robust Landau-Zener sweeps through an avoided crossing. In the case where the avoided crossing is purely noise-induced, we prove that operations based on monotonic sweeps cannot be robust to noise. Hence, we design families of phase gates based on non-monotonic drives that are error-robust up to second order. In the general case where there is an avoided crossing even in the absence of noise, we present a general technique for designing robust driving protocols that takes advantage of a relationship between the Landau-Zener problem and space curves of constant torsion.
Under resonant conditions, a long sequence of landau-zener transitions can lead to Rabi oscillations. Using a nitrogen-vacancy (NV) center spin in diamond, we investigated the interference between more than 100 Landau-Zener processes. We observed the new type of Rabi oscillations of the electron spin resulting from the interference between successive Landau-Zener processes in various regimes, including both slow and fast passages. The combination of the control techniques and the favorable coherent properties of NV centers provides an excellent experimental platform to study a variety of quantum dynamical phenomena.
Probabilities deduced from quantum information studies are usually based on averaging many identical experiments separated by an initialization step. Such initialization steps become experimentally more challenging to implement as the complexity of quantum circuits increases. To better understand the consequences of imperfect initialization on the deduced probabilities, we study the effect of not initializing the system between measurements. For this we utilize Landau-Zener-Stuckelberg oscillations in a double quantum dot circuit. Experimental results are successfully compared to theoretical simulations.
We study the effect of Landau-Zener (LZ) tunneling caused by the varying sweeping rate of external field, formulating and approximately solving the problem with many levels of the LZ tunneling rate. Comparing with the steadily vary about sweeping field, the LZ tunneling rate will be essentially changed because of the unsteady variation of the sweeping field in time. Thus could help us to make the particles with in lower states transit periodically to upper states within the finite time.
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