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arXiv:cond-mat/0207005 · Physical review. B, Condensed matter

Quantum dynamics in nonequilibrium strongly correlated environments

M. B. Hastings, Ivar Martin, Dmitry Mozyrsky

Published Jul 1, 2003• 10 citations
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Abstract

We consider a biased quantum point contact between two Luttinger liquids measuring a quantum-mechanical system (oscillator). There are three main physical results. First, we find that for voltages higher than the oscillator level spacing, the effect of the measurement is equivalent to coupling to a heat bath, with an effective temperature that only depends on the device $I\ensuremath{-}V$ characteristic. Second, we find that this heating changes the $I\ensuremath{-}V$ characteristics on the junction. Finally, we predict a modulation of the tunneling current at the oscillator frequency. Also, we find that a generalized nonequilibrium fluctuation-dissipation relation connects the decoherence and dissipation of the oscillator to the current-voltage characteristics of the device.

DOI
10.1103/physrevb.68.035101

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We consider a biased quantum point contact between two Luttinger liquids measuring a quantum-mechanical system (oscillator). There are three main physical results. First, we find that for voltages higher than the oscillator level spacing, the effect of the measurement is equivalent to coupling to a heat bath, with an effective temperature that only depends on the device I\ensuremath−VI\ensuremath{-}VI\ensuremath−V characteristic. Second, we find that this heating changes the I\ensuremath−VI\ensuremath{-}VI\ensuremath−V characteristics on the junction. Finally, we predict a modulation of the tunneling current at the oscillator frequency. Also, we find that a generalized nonequilibrium fluctuation-dissipation relation connects the decoherence and dissipation of the oscillator to the current-voltage characteristics of the device.
We find the nonlinear conductance of a dissipative resonant level in the nonequilibrium steady state near its quantum critical point. The system consists of a spin-polarized quantum dot connected to two resistive leads that provide ohmic dissipation. We focus on the crossover from the strong-coupling, non-Fermi-liquid regime to the weak-coupling, Fermi-liquid ground state, a crossover driven by the instability of the quantum critical point to hybridization asymmetry or detuning of the level in the dot. We show that the crossover properties are given by tunneling through an effective single barrier described by the boundary sine-Gordon model. The nonlinear conductance is then obtained from thermodynamic Bethe ansatz results in the literature, which were developed to treat tunneling in a Luttinger liquid. The current-voltage characteristics are thus found for any value of the resistance of the leads. For the special case of lead resistance equal to the quantum resistance, we find mappings onto, first, the two-channel Kondo model and, second, an effectively noninteracting model from which the nonlinear conductance is found analytically. A key feature of the general crossover function is that the nonequilibrium crossover driven by applied bias is different from the crossover driven by temperature---we find that the nonequilibrium crossover is substantially sharper. Finally, we compare to experimental results for both the bias and temperature crossovers: the agreement is excellent.
A model of an electrical tunnel junction coupled to a mechanical system (oscillator) is studied to simulate the dephasing effect of measurement on a quantum system. The problem is solved at zero temperature under conditions of strong nonequilibrium in the measurement apparatus. For linear coupling between the oscillator and tunneling electrons, it is found that the oscillator dynamics becomes damped, with the effective temperature determined by the voltage drop across the junction. It is demonstrated that both the quantum heating and the quantum damping of the oscillator manifest themselves in the current-voltage characteristic of the tunnel junction.
This thesis is concerned with employing the statistics of charge transfer in a conductor as a tool for quantum measurement. The physical systems studied are electronic devices made by nanoscale manufacturing techniques. In this context quantum measurement appears not as a postulate, but as physical process. In this thesis I am considering a quantum system, in particular a qubit or a nanomechanical resonator, interacting with a tunnel junction. The effect of coupling a quantum system to a tunnel junction is twofold: The state of the quantum system will be changed and there will be information about the quantum system in the statistics of charge transfer of the tunnel junction. As the first example a quantum measurement process of a qubit is considered. A common description of the system and charge dynamics is found by introducing a new quantity, the charge specific density matrix. By deriving and solving a Markovian master equation for this quantity the measurement process is analyzed. The measurement is shown to be a dynamical process, where correlations between the initial state of the qubit and the number of charges transferred in the tunnel junction arise on a typical timescale, the measurement time. As another example of a quantum system a nanomechanical oscillator is considered. It is found, that the biased tunnel junction, acting as a non-equilibrium environment to the oscillator, increases the temperature of the oscillator from its thermal equilibrium value. The current in the junction is modulated by the interaction with the oscillator, but the influence vanishes for bias voltages smaller than the oscillator frequency. For an asymmetric junction and non-vanishing oscillator momentum a current is shown to flow through the junction even at zero bias. The current noise spectrum induced by the oscillator in the tunnel junction consists of a noise floor and a peaked structure with peaks at zero frequency, the oscillator frequency and double the oscillator frequency. The peak heights are dependent on the coupling strength between oscillator and junction, the occupation number of the oscillator, the bias voltage and the junction temperature. I show how the peak height can be used as a measure of the oscillator temperature, demonstrating that the noise of a tunnel junction can be used for electronic thermometry of a nanomechanical oscillator.
We compute exactly the nonequilibrium dc noise in a Luttinger liquid with an impurity and an applied voltage. By generalizing Landauer transport theory for Fermi liquids to interacting, integrable systems, we relate this noise to the density fluctuations of quasiparticles. We then show how to compute these fluctuations using the Bethe ansatz. The nontrivial density correlations from the interactions result in a substantial part of the nonequilibrium noise. The final result for the noise is a scaling function of the voltage, temperature, and impurity coupling. It may eventually be observable in tunneling between edges of a fractional quantum Hall effect device. \textcopyright{} 1996 The American Physical Society.
We consider the effect of electron-electron interactions on a voltage biased quantum point contact in the tunneling regime used as a detector of a nearby qubit. We model the leads of the quantum point contact as Luttinger liquids, incorporate the effects of finite temperature and analyze the detection-induced decoherence rate and the detector efficiency, QQQ. We find that interactions generically reduce the induced decoherence along with the detector's efficiency, and strongly affect the relative strength of the decoherence induced by tunneling and that induced by interactions with the local density. With increasing interaction strength, the regime of quantum-limited detection ($Q\ensuremath{\rightarrow}1$) is shifted to increasingly lower temperatures or higher bias voltages respectively. For small to moderate interaction strengths, QQQ is a monotonously decreasing function of temperature as in the noninteracting case. Surprisingly, for sufficiently strong interactions we identify an intermediate temperature regime where the efficiency of the detector increases with rising temperature.
We theoretically investigate the nonequilibrium current through a quantum dot coupled to one-dimensional electron leads, utilizing a controlled frequency-dependent renormalization group approach. We compute the nonequilibrium conductance for large bias voltages and address the interplay between decoherence, Kondo entanglement, and Luttinger physics. The combined effect of large bias voltage and strong interactions in the leads, known to stabilize two-channel Kondo physics, results in nontrivial modifications in the conductance. Interestingly, these unusual changes in the conductance persist in the presence of a finite channel asymmetry.