Driven tunneling: New possibilities for coherent and incoherent quantum transport

In the spectrum of systems showing chaos-assisted tunneling, three-state crossings are formed when a chaotic singlet intersects a tunnel doublet. We study the dissipative quantum dynamics in the vicinity of such crossings. A harmonically driven double well coupled to a bath serves as a model. Markov and rotating-wave approximations are introduced with respect to the Floquet spectrum of the time-dependent central system. The resulting master equation is integrated numerically. We find various types of transient tunneling, determined by the relation of the level width to the inherent energy scales of the crossing. The decay of coherent tunneling can be significantly retarded or accelerated. Modifications of the quantum asymptotic state by the crossing are also studied. The comparison with a simple three-state model shows that in contrast to the undamped case, the participation of states outside the crossing cannot be neglected in the presence of dissipation. 42.50.Lc, 03.65.Sq Typeset using REVT E X

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“…yields for the matrix elements σ αβ of the reduced density matrix ρ S the equation of motion [18,19,21,23]σ…”

Section: Born-markov Approximationmentioning

confidence: 99%

“…We treat the quantum dissipative dynamics within the framework of the Floquet formalism [18][19][20][21][22][23]. In the present context of an interplay of tunneling with incoherent processes, we focus on the regime of weak dissipation.…”

Section: Introductionmentioning

confidence: 99%

Coherent and incoherent chaotic tunneling near singlet-doublet crossings

et al. 1998

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“…In general, this time scale gets shorter for higher temperatures, reflecting the growth of the transition rates (53) [36]. However, there exist counterintuitive effects: For driven tunneling in the vicinity of an exact crossing of the ground-state doublet, the coherent suppression of tunneling [22,32,33] can be stabilized with higher temperatures [37][38][39] until levels outside the doublet start to play a rôle. So far, we have considered only driving frequencies much smaller than the frequency scale ω 0 of the relevant classical resonances, i.e., a parameter regime where classical motion is predominantly regular.…”

Section: Tunneling Driving and Dissipationmentioning

confidence: 99%

“…yields the equation of motion for the elements ρ αβ of the reduced density matrix ρ S [37,39,52,54],…”

Section: Master Equationmentioning

confidence: 99%

“…In general, for driven tunneling in the weakly damped regime, this time scale gets shorter for higher temperatures, as transition rates grow [36]. However, in the vicinity of an exact crossing of the ground-state quasienergies, the coherent suppression of tunneling [22,32,33] can be stabilized with higher temperatures [37][38][39] and increasing friction [55,56] until levels outside the doublet start to play a rôle. We have studied dissipative chaos-assisted tunneling, at the particular real singlet-doublet crossing introduced in Sec.…”

Section: Chaos-assisted Dissipative Tunnelingmentioning

confidence: 99%

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Driven Tunneling: Chaos and Decoherence

Hänggi

Kohler

Dittrich

Statistical and Dynamical Aspects of Mesoscopic Systems

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Abstract. Chaotic tunneling in a driven double-well system is investigated in absence as well as in the presence of dissipation. As the constitutive mechanism of chaosassisted tunneling, we focus on the dynamics in the vicinity of three-level crossings in the quasienergy spectrum. They are formed when a tunnel doublet, located on a pair of symmetry-related tori in the classical phase space, approaches a chaotic singlet in energy. The coherent quantum dynamics near the crossing, in particular the enhanced tunneling that involves the chaotic singlet state as a "step stone", is described satisfactorily by a three-state model. It fails, however, for the corresponding dissipative dynamics, because incoherent transitions due to the interaction with the environment indirectly couple the three states in the crossing to the remaining quasienergy states. We model dissipation by coupling the double well, the driving included, to a heat bath. The time dependence of the central system, with a quasienergy spectrum containing exponentially small tunnel splittings, requires special considerations when applying the Born-Markov and rotating-wave approximations to derive a master equation for the density operator. We discuss the effect of decoherence on the now transient chaosassisted tunneling: While decoherence is accelerated practically independent of temperature near the center of the crossing, it can be stabilzed with increasing temperature at a chaotic-state induced exact crossing of the ground-state quasienergies. Moreover the asymptotic amount of coherence left within the vicinity of the crossing is enhanced if the temperature is below the splitting of the avoided crossing; but becomes diminished when temperature raises above the splitting (chaos-induced coherence or incoherence, respectively). The asymptotic state of the driven dissipative quantum dynamics partially resembles the, possibly strange, attractor of the corresponding damped driven classical dynamics, but also exhibits characteristic quantum effects.

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Asymptotic Floquet states of open quantum systems: the role of interaction

et al. 2017

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When a periodically modulated many-body quantum system is weakly coupled to an environment, the combined action of these temporal modulations and dissipation steers the system towards a state characterized by a time-periodic density operator. To resolve this asymptotic non-equilibrium state at stroboscopic instants of time, we use the dissipative propagator over one period of modulations, 'Floquet map', and evaluate the stroboscopic density operator as its invariant. Particle interactions control properties of the map and thus the features of its invariant. In addition, the spectrum of the map provides insight into the system relaxation towards the asymptotic state and may help to understand whether it is possible (or not) to construct a stroboscopic time-independent Lindblad generator which mimics the action of the original time-dependent one. We illustrate the idea with a scalable many-body model, a periodically modulated Bose-Hubbard dimer. We contrast the relations between the interaction-induced bifurcations in a mean-field description with the numerically exact stroboscopic evolution and discuss the characteristics of the genuine quantum many-body state vs the characteristics of its mean-field counterpart.

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Driven tunneling: New possibilities for coherent and incoherent quantum transport

Cited by 3 publications

References 41 publications

Coherent and incoherent chaotic tunneling near singlet-doublet crossings

Coherent and incoherent chaotic tunneling near singlet-doublet crossings

Driven Tunneling: Chaos and Decoherence

Asymptotic Floquet states of open quantum systems: the role of interaction

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