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arXiv:1705.04512 · Physical Review Letters

Landau-Zener Transition in a Continuously Measured Single-Molecule Spin Transistor

Filippo Troiani, Clément Godfrin, Stefan Thiele, Franck Balestro, Wolfgang Wernsdorfer, Svetlana V. Klyatskaya, Mario Ruben, M. Affronte

Published Jun 23, 2017• 24 citations
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Abstract

We monitor the Landau-Zener dynamics of a single-ion magnet inserted into a spin-transistor geometry. For increasing field-sweep rates, the spin reversal probability shows increasing deviations from that of a closed system. In the low-conductance limit, such deviations are shown to result from a dephasing process. In particular, the observed behaviors are successfully simulated by means of an adiabatic master equation, with time averaged dephasing (Lindblad) operators. The time average is tentatively interpreted in terms of the finite time resolution of the continuous measurement.

DOI
10.1103/physrevlett.118.257701

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We monitor the Landau-Zener dynamics of a single-ion magnet inserted into a spin-transistor geometry. For increasing field-sweep rates, the spin reversal probability shows increasing deviations from that of a closed system. In the low-conductance limit, such deviations are shown to result from a dephasing process. In particular, the observed behaviors are successfully simulated by means of an adiabatic master equation, with time averaged dephasing (Lindblad) operators. The time average is tentatively interpreted in terms of the finite time resolution of the continuous measurement.
Decoherence processes in crystals of molecular magnets are prototypical for interacting electronic spin systems. We analyze the Landau-Zener dynamics of the archetypical TbPc2{\mathrm{TbPc}}_{2}TbPc2​ complex diluted in a diamagnetic monocrystal. The dependence of the tunneling probability on the field sweep rate is evaluated in the framework of the recently proposed master equation in which the decoherence processes are described through a phenomenological Lindblad operator. Thus, we showcase low-temperature magnetic measurements that complement resonant techniques in determining small tunnel splittings and dephasing times.
It is shown that in experiments on single molecule magnets in which transitions between two lowest spins states are induced by sweeping the applied magnetic field along the easy axis; the transitions are fully incoherent. Nuclear spins and the dipolar coupling of molecular spins are identified as the main sources of decoherence, and the form of the decoherence is calculated. The Landau-Zener-St\"uckelberg (LZS) process is examined in light of this decoherence, and it is shown that the correct formula for the spin-flip probability is better given by a more recent formula of Kayanuma than that of LZS. The two formulas are shown to be identical in the limit of rapid sweeps. An approximate way of incorporating the molecular spin dipole field into the rate equations for this process is developed.
An innovative microscopic model with a minimal number of parameters: tunneling splitting gap, external field sweeping velocity, and decoherence rate is used to describe dynamics of the dissipative Landau-Zener transition in the presence of the decoherence. In limiting cases, the derived equation of motion gives rise to the well-known Landau-Zener and Kayanuma formula. In a general case, the description demonstrates a non-monotonic flipping probability with respect to the sweeping velocity, which is also found in some other models. This non-monotony can be explained by considering the competition and timescale of the quantum tunneling, crossing period, and decoherence process. The simplicity and robustness of the theory offer a practical and novel description of the Landau-Zener transition. In addition, it promises an alternative method to the electron paramagnetic resonance in measuring the effective decoherence rate of relevant quantum systems.
The time evolution and the asymptotic outcome of a Landau–Zener–Stueckelberg–Majorana (LZ) process under continuous weak non-selective measurement is analyzed. We compare two measurement protocols in which the populations of either the adiabatic or the non-adiabatic levels are (continuously and weakly) monitored. The weak measurement formalism, described using a Gaussian Kraus operator, leads to a time evolution characterized by a Markovian dephasing process, which, in the non-adiabatic measurement protocol is similar to earlier studies of LZ dynamics in a dephasing environment. Casting the problem in the language of measurement theory makes it possible for us to compare diabatic and adiabatic measurement scenarios, to consider engineered dephasing as a control device and to examine the manifestation of the Zeno effect under the different measurement protocols. In particular, under measurement of the non-adiabatic populations, the Zeno effect is manifested not as a freezing of the measured system in its initial state, but rather as an approach to equal asymptotic populations of the two diabatic states. This behavior can be traced to the way by which the weak measurement formalism behaves in the strong measurement limit, with a built-in relationship between measurement time and strength.
The Landau-Zener (LZ) transition is one of the most fundamental phenomena in quantum dynamics. It describes nonadiabatic transitions between quantum states near an avoided crossing that can occur in diverse physical systems. Here we report experimental measurements and tuning of LZ transitions between the dressed eigenlevels of a Bose-Einstein condensate (BEC) that is synthetically spin-orbit (SO) coupled. We measure the transition probability as the BEC is accelerated through the SO avoided crossing and study its dependence on the coupling between the diabatic (bare) states, eigenlevel slope, and eigenstate velocity---the three parameters of the LZ model that are independently controlled in our experiments. Furthermore, we performed time-resolved measurements to demonstrate the breaking down of the spin-momentum locking of the spin-orbit-coupled BEC in the nonadiabatic regime, and we determined the diabatic switching time of the LZ transitions. Our observations show quantitative agreement with the LZ model and numerical simulations of the quantum dynamics in the quasimomentum space. The tunable LZ transition may be exploited to enable a spin-dependent atomtronic transistor.
Motivated by recent cold-atom experiments in optical lattices, we consider a lattice version of the Landau-Zener problem. Every single site is described by a Landau-Zener problem, but due to particle tunneling between neighboring lattice sites this on-site single-particle Landau-Zener dynamics couples to the particle motion within the lattice. The lattice, apart from having a dephasing effect on single-site Landau-Zener transitions, also implies, in the presence of a confining trap, an intersite particle flow induced by the Landau-Zener sweeping. This gives rise to an interplay between intra- and intersite dynamics. The adiabaticity constraint is therefore not simply given by the standard one, the Hamiltonian rate of change relative to the gap of the on-site problem. In experimentally realistic situations, the full system evolution is well described by Franck-Condon physics; e.g., nonadiabatic excitations are predominantly external ones characterized by large phononic vibrations in the atomic cloud, while internal excitations are very weak as close-to-perfect on-site transitions take place.