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AIP conference proceedings

Quantum steps in hysteresis loops

Michael Thorwart, Peter Reimann, Peter Jung

Published Jan 1, 1997• 0 citations
Publisher

Abstract

We are studying bistable quantum systems coupled to a thermal environment and driven by a strong external force. Thermal and quantum effects on the switching hysteresis are studied numerically by evaluating a time-dependent real-time double path-integral with the recently developed iterative tensor multiplication scheme for the Quasi-adiabatic path-integral propagator method. For temperatures below the quantum-classical crossover temperature, the response of the system exhibits steps for slow external driving. We show that these steps are due to dissipative resonant tunneling and appear in the vicinity of avoided level-crossings of the spectrum of the undamped Hamiltonian. We discuss possible relations to the recently discovered hysteresis steps in organic high-spin molecules.

DOI
10.1063/1.54220

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We are studying bistable quantum systems coupled to a thermal environment and driven by a strong external force. Thermal and quantum effects on the switching hysteresis are studied numerically by evaluating a time-dependent real-time double path-integral with the recently developed iterative tensor multiplication scheme for the Quasi-adiabatic path-integral propagator method. For temperatures below the quantum-classical crossover temperature, the response of the system exhibits steps for slow external driving. We show that these steps are due to dissipative resonant tunneling and appear in the vicinity of avoided level-crossings of the spectrum of the undamped Hamiltonian. We discuss possible relations to the recently discovered hysteresis steps in organic high-spin molecules.
We are studying bistable quantum systems coupled to a thermal environment in the presence of an external controlling force. The impact of thermal and quantum effects on the switching hysteresis is studied by evaluating a time-dependent real-time double path integral with the recently developed iterative tensor multiplication scheme for the quasiadiabatic path integral propagator method for temperatures ranging from well above to well below quantum-classical crossover temperature. The switching dynamics and its intimate connection to quantum stochastic resonance is studied here for the first time without limitation to a two-state description and/or small external forces.
A new approach to the magnetic hysteresis loop and magnetization relaxation of molecule magnet, Mn12, is presented. The method, so called "quasi-thermal equilibrium (QTE) + erase phase (EP)" (QTE + EP), leads the dissipation in state evolution. The method gives an method to approach an irreversible quantum dynamic tunnelling and time evolution of system and straightly leads the hysteresis loops. The QTE can work well for the double-well system and is able to be extended to the multi-wells quantum system. The EP is based on the physics of random interaction with the environment that results the phase de-coherence or say "re-initial" of the phase of quantum state during the time evolution. The stairs in the magnetic loops of Mn12 we have obtained quantitatively show the quantum resonant tunnelling. The relaxation of magnetization from initial lowest state is calculated for different temperatures and well shows the exponential behavior. The theoretical results well agree with the experiments.
In this PhD thesis we have been concerned with dissipative and decoherence processes which take place specifically for quantum systems in a dissipative bistable potential. This potential describes a Hamiltonian system whose spectrum is composed by a ladder of levels, grouped as doublets under the potential barrier and being almost equally spaced above it. The system interacts with a thermal environment, fully characterized by the so-called bath spectral density. The dynamical quantity we looked at is the so-called reduced density matrix (RDM), obtained by tracing out the full density matrix the environmental degrees of freedom. The matrix elements for the RDM are exactly evaluated by means of the Feynman-Vernon real-time path-integral technique. Depending on which regime of parameters we are interested in, i.e. temperature and coupling strength with the reservoir, a few or several energy levels contribute to the dynamics. In particular, a two-level system (TLS) is first analyzed, corresponding to the regime where only the lowest doublet is energetically accessible. We discussed in the beginning the case of a TLS interacting with Ohmic and super-Ohmic baths and then the situation in which a symmetric TLS is assumed to be coupled with an external detector, like a dc-SQUID, the latter being coupled to an Ohmic environment. This model provides a better description of a real qubit, as frequently discussed in various experiments. In the former case, we developed a theory called Weakly-Interacting Blip Approximation (WIBA), which is nonperturbative in the coupling strength as well as in the tunneling frequency and gives reliable results over a wide range of temperatures and coupling strength to the thermal environment. In the latter case, the dynamics was evaluated upon starting from the Non-Interacting Blip Approximation (NIBA) and approximating the NIBA kernels up to first order in the detector-bath coupling strength. Analytical results, valid also at finite detuning, were obtained and we showed that our theory correctly reproduces the onset of multiple oscillation frequencies in the dynamics due to the entanglement between TLS and detector. Finally, we discussed the more general case of an M-level system coupled with an Ohmic environment. This situation describes the case of a bistable potential where the temperature is high enough that higher-lying energy levels are being populated and the system cannot be reduced to a simple TLS. Many are the experimental situations which can be described by our theory. We developed a novel approximation called Weakly-Interacting VR-Blip Approximation (VR-WIBA) for the dynamics in a driven dissipative bistable potential. In the regimes of low to moderate temperatures and coupling strengths, we exploited a separation of time scales between tunneling and vibrational relaxation events and we could derive analytical kernels for the intra- and inter-well dynamics.
The dissipative dynamics of a quantum bistable system coupled to a Ohmic heat bath is investigated beyond the spin-boson approximation. Within the path-integral approach to quantum dissipation, we propose an approximation scheme which exploits the separation of time scales between intra- and interwell (tunneling) dynamics. The resulting generalized master equation for the populations in a space localized basis enables us to investigate a wide range of temperatures and system-environment coupling strengths. A phase diagram in the coupling-temperature space is provided to give a comprehensive account of the different dynamical regimes.
Recent progress in numerical methods for evaluating the real-time path integral in dissipative harmonic environments is reviewed. Quasi-adiabatic propagators constructed numerically allow convergence of the path integral with large time increments. Integration of the harmonic bath leads to path integral expressions that incorporate the exact dynamics of the quantum particle along the adiabatic path, with an influence functional that describes nonadiabatic corrections. The resulting quasi-adiabatic propagator path integral is evaluated by efficient system-specific quadratures in most regimes of parameter space, although some cases are handled by grid Monte Carlo sampling. Exploiting the finite span of nonlocal influence functional interactions characteristic of broad condensed phase spectra leads to an iterative scheme for calculating the path integral over arbitrary time lengths. No uncontrolled approximations are introduced, and the resulting methodology converges to the exact quantum result with modest amounts of computational power. Applications to tunneling dynamics in the condensed phase are described.