Competition between relaxation and external driving in the dissipative Landau–Zener problem

Nalbach, P.; Thorwart, Michael

doi:10.1016/j.chemphys.2010.05.007

Cited by 27 publications

(37 citation statements)

References 43 publications

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“…In any realistic system the quantum system is subjected to external fluctuating forces which result typically in decoherence and relaxation [12,13]. The according rate constitutes an additional time scale which competes with the driving to determine the dynamics [14,15].…”

Section: Introductionmentioning

confidence: 99%

Adiabatic-Markovian bath dynamics at avoided crossings

Nalbach

2014

Phys. Rev. A

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We investigate the dissipative influence of environmental fluctuations on the dynamics of driven quantum systems at an avoided crossing. We derive two simple approximative equations valid for weak system-bath coupling and compare results for the dissipative Landau-Zener problem with numerically exact results. Very good agreement is found for slow, i.e., adiabatic, driving. Specifically, the minimum in the Landau-Zener probability resulting from the competition of driving and dissipation is well described. For system-bath couplings and temperatures, where this minimum is observed in the adiabatic driving regime, good agreement is also observed for fast driving when the dynamics tends toward nonadiabatic behavior. Otherwise, however, for large temperatures and fast driving our approximation fails even for weak system-bath couplings, for which an undriven system is still accurately described by weak-coupling approximations.

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Section: Introductionmentioning

confidence: 99%

Adiabatic-Markovian bath dynamics at avoided crossings

Nalbach

2014

Phys. Rev. A

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“…We determine the dissipative nonequilibrium real time dynamics (initialized by applying voltage pulses) by deriving effective nonequilibrium Bloch equations (NBEs). These allow fast numerical treatment in contrast to numerical exact methods [8,9] and thus allow a comphrehensive analysis of recent experiments by Petersson et al [1] and Dovzhenko et al [12]. In these experiments quantum control of a single electron was achieved by means of applying ultra short voltage pulses to control gates of the laterally defined DQD.…”

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confidence: 99%

“…Many fluctuation sources of the noisy solid state environment, which act on the electron in the DQD and thus destroy coherence, were revealed but a comphrehensive picture is elusive. Furthermore, driving by voltage pulses causes an intrinsic nonequilibrium situation in which relaxation competes with driving [8][9][10] which renders a theoretical description of the dissipative nonequilibrium dynamics highly nontrivial.…”

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confidence: 99%

“…the regime of competition between driving and relaxation, for weak DQD-environment coupling. We ensured this by extensive comparisson with numerical exact results [8,9]. Details will be presented elsewhere.…”

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confidence: 99%

“…Driven dissipative dynamics Including dissipation into the driven dynamics of the DQD causes a competition between driving and relaxation [8,9] which renders all but expansive numerical treatments inadequate. Following the standard approach within open quantum dynamics [11] we couple the driven two-level Hamiltonian (1) of the DQD to environmental fluctuations described by harmonic oscillators.…”

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Nonequilibrium Landau-Zener-Stueckelberg spectroscopy in a double quantum dot

2013

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We study theoretically nonequilibrium Landau-Zener-Stückelberg (LZS) dynamics in a driven double quantum dot (DQD) including dephasing and, importantly, energy relaxation due to environmental fluctuations. We derive effective nonequilibrium Bloch equations. These allow us to identify clear signatures for LZS oscilations observed but not recognized as such in experiments [Petersson et al., Phys. Rev. Lett. 105, 246804, 2010] and to identify the full environmental fluctuation spectra acting on a DQD given experimental data as in [Petersson et al., Phys. Rev. Lett. 105, 246804, 2010]. Herein we find that super-Ohmic fluctuations, typically due to phonons, are the main relaxation channel for a detuned DQD whereas Ohmic fluctuations dominate at zero detuning.PACS numbers: 03.65. Yz,85.35.Gv,73.21.La Quantum electronic devices, as qubits realized by double quantum dots (DQD), require coherence times which exceed their quantum operation time during which the DQD is typically strongly driven by external voltage pulses. Tremendous research efforts studied semiconductor based devices to achieve coherent quantum control [1][2][3][4][5][6][7]. Many fluctuation sources of the noisy solid state environment, which act on the electron in the DQD and thus destroy coherence, were revealed but a comphrehensive picture is elusive. Furthermore, driving by voltage pulses causes an intrinsic nonequilibrium situation in which relaxation competes with driving [8-10] which renders a theoretical description of the dissipative nonequilibrium dynamics highly nontrivial.Here, we theoretically study the dissipative nonequilibrium dynamics of a single electron charge qubit defined in a DQD embedded in a noisy solid state environment driven by voltage pulses. While DQD charge qubits have relatively short coherence times, this disadvantage is compensated by the possibility of fast quantum operations. We model the DQD and its dissipation as a quantum two-level system in an open quantum system approach [11]. We determine the dissipative nonequilibrium real time dynamics (initialized by applying voltage pulses) by deriving effective nonequilibrium Bloch equations (NBEs). These allow fast numerical treatment in contrast to numerical exact methods [8,9] and thus allow a comphrehensive analysis of recent experiments by Petersson et al. [1] and Dovzhenko et al. [12]. In these experiments quantum control of a single electron was achieved by means of applying ultra short voltage pulses to control gates of the laterally defined DQD. In these time ensemble measurements the DQD was cycled (with 40 MHz repetition rate) between two different ground state configurations while its average charge occupation was continuously detected via the electric current through a capacitively coupled quantum point contact (QPC). The applied voltage pulses generate Landau-Zener-Stückelberg (LZS) dynamics [13] and we can identify so far unexplained features in the experimental data as signatures of coherent LZS oscillations.In the experimental ensemble measurements the de...

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Stueckelberg Oscillations in a Two‐State Two‐Path Model of a Conical Intersection

et al. 2016

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The two-state two-path model is introduced as a minimized model to describe the quantum dynamics of an electronic wave packet in the vicinity of a conical intersection. It involves two electronic potential energy surfaces each of which hosts a pair of quasi-classical trajectories over which the wave packet is assumed to be delocalized. When both trajectories evolve dynamically either diabatically or adiabatically, the full wave packet dynamics shows only features of the dynamics around avoided level crossings in the vicinity of the conical intersection. When one trajectory evolves adiabatically whereas the other trajectory follows a diabatic evolution, quantum mechanical interference of the wave packet components on each path generates Stueckelberg oscillations in the transition probability. These are surprisingly robust against a dissipative environment and, thus, should be a marker for conical intersections.

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Competition between relaxation and external driving in the dissipative Landau–Zener problem

Cited by 27 publications

References 43 publications

Adiabatic-Markovian bath dynamics at avoided crossings

Adiabatic-Markovian bath dynamics at avoided crossings

Nonequilibrium Landau-Zener-Stueckelberg spectroscopy in a double quantum dot

Stueckelberg Oscillations in a Two‐State Two‐Path Model of a Conical Intersection

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