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Inelastic tunneling in a double quantum dot coupled to a bosonic environment

Fujisawa, T., Wilfred G. van der Wiel, Leo P. Kouwenhoven, 藤澤利正, T. Fujisawa

Published Nov 1, 2018• 16 citations
OpenAlex

Abstract

Coupling a quantum system to a bosonic environment always give rise to inelastic processes, which reduce the coherency of the system. We measure energy-dependent rates for inelastic tunneling processes in a fully controllable two-level system of a double quantum dot. The emission and absorption rates are well reproduced by Einstein's coefficients, which relate to the spontaneous emission rate. The inelastic tunneling rate can be comparable to the elastic tunneling rate if the boson occupation number becomes large. In the specific semiconductor double dot, the energy dependence of the inelastic rate suggests that acoustic phonons are coupled to the double dot piezoelectrically.

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Coupling a quantum system to a bosonic environment always give rise to inelastic processes, which reduce the coherency of the system. We measure energy-dependent rates for inelastic tunneling processes in a fully controllable two-level system of a double quantum dot. The emission and absorption rates are well reproduced by Einstein's coefficients, which relate to the spontaneous emission rate. The inelastic tunneling rate can be comparable to the elastic tunneling rate if the boson occupation number becomes large. In the specific semiconductor double dot, the energy dependence of the inelastic rate suggests that acoustic phonons are coupled to the double dot piezoelectrically.
A double quantum dot device is a tunable two-level system for electronic energy states. A dc electron current was used to directly measure the rates for elastic and inelastic transitions between the two levels. For inelastic transitions, energy is exchanged with bosonic degrees of freedom in the environment. The inelastic transition rates are well described by the Einstein coefficients, relating absorption with stimulated and spontaneous emission. The most effectively coupled bosons in the specific environment of the semiconductor device used here were acoustic phonons. The experiments demonstrate the importance of vacuum fluctuations in the environment for quantum dot devices and potential design constraints for their use for preparing long-lived quantum states.
The interaction between a qubit and its environment provides a channel for energy relaxation which has an energy-dependent timescale governed by the specific coupling mechanism. We measure the rate of inelastic decay in a Si MOS double quantum dot (DQD) charge qubit through sensing the charge state's response to non-adiabatic driving of its excited state population. The charge distribution is sensed remotely in the weak measurement regime. We extract emission rates down to kHz frequencies by measuring the variation of the non-equilibrium charge occupancy as a function of amplitude and dwell times between non-adiabatic pulses. Our measurement of the energy-dependent relaxation rate provides a fingerprint of the relaxation mechanism, indicating that relaxation rates for this Si MOS DQD are consistent with coupling to deformation acoustic phonons.
Hole-phonon interactions play an important role in transport and decoherence processes in semiconductor quantum dots. Here we investigate hole-phonon coupling in a gate-defined GaAs double quantum dot integrated with a quantum point contact charge sensor. Under finite source-drain bias, pronounced oscillatory stripe patterns appear near specific charge transition regions in the charge stability diagram. We attribute these oscillations to phonon emission during inelastic interdot tunneling. A theoretical model including piezoelectric hole-phonon coupling reproduces the observed patterns. Furthermore, our analysis shows that the oscillations emerge only in particular charge configurations. Our results provide direct insight into phonon-assisted transport and coherent hole-phonon interactions in semiconductor quantum dots.
The dynamics of charge qubit in a double quantum dot coupled to phonons is investigated theoretically in terms of a perturbation treatment based on a unitary transformation. The dynamical tunneling current is obtained explicitly. The decoherence induced by acoustic phonons is analyzed in detail after a derivation of spectral density. It is shown that the contribution from deformation potential coupling is comparable to that from piezoelectric coupling in small dots and large tunneling rates. A possible decoupling mechanism is predicted.
We study a voltage biased InAs double quantum dot (DQD) that is coupled to a superconducting transmission line resonator. Inelastic tunneling in the DQD is mediated by electron phonon coupling and coupling to the cavity mode. We show that electronic transport through the DQD leads to photon emission from the cavity at a rate of 10 MHz. With a small cavity drive field, we observe a gain of up to 15 in the cavity transmission. Our results are analyzed in the context of existing theoretical models and suggest that it may be necessary to account for inelastic tunneling processes that proceed via simultaneous emission of a phonon and a photon.