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arXiv:cond-mat/0105519

Decoherence from Vacuum Fluctuations

Μ. Büttiker

Published May 28, 2001• 2 citations
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Abstract

Vacuum fluctuations are a source of irreversibility and decoherence. We investigate the persistent current and its fluctuations in a ring with an in-line quantum dot with an Aharonov-Bohm flux through the hole of the ring. The Coulomb blockade leads to persistent current peaks at values of the gate voltage at which two charge states of the dot have the same free energy. We couple the structure to an external circuit and investigate the effect of the zero-temperature (vacuum fluctuations) on the ground state of the ring. We find that the ground state of the ring undergoes a crossover from a state with an average persistent current much larger than the (time-dependent) mean squared fluctuations to a state with a small average persistent current and large mean squared fluctuations. We discuss the spectral density of charge fluctuations and discuss diffusion rates for angle variables characterizing the ground state in Bloch representation.

DOI
10.48550/arxiv.cond-mat/0105519

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Vacuum fluctuations are a source of irreversibility and decoherence. We investigate the persistent current and its fluctuations in a ring with an in-line quantum dot with an Aharonov-Bohm flux through the hole of the ring. The Coulomb blockade leads to persistent current peaks at values of the gate voltage at which two charge states of the dot have the same free energy. We couple the structure to an external circuit and investigate the effect of the zero-temperature (vacuum fluctuations) on the ground state of the ring. We find that the ground state of the ring undergoes a crossover from a state with an average persistent current much larger than the (time-dependent) mean squared fluctuations to a state with a small average persistent current and large mean squared fluctuations. We discuss the spectral density of charge fluctuations and discuss diffusion rates for angle variables characterizing the ground state in Bloch representation.
We investigate the role of vacuum (zero-point) fluctuations in generating decoherence in a number of simple models. First we discuss a harmonic oscillator coupled to a semi-infinite elastic string and discuss the irreversible nature of such a bath. We investigate the fluctuations in energy of the oscillator and discuss the trace the oscillator leaves in the bath. Most of the work deals with two-level systems coupled to a bosonic bath (a transmission line). For two-level systems with a Hamiltonian that commutes with the total Hamiltonian (system plus coupling plus bath) the ground state is a pure state. The energy of the system is a constant of motion. For the general case, the energy of the two-level system fluctuates, and the ground state is only partially coherent. A particular realization of such a two level system consists of a mesoscopic ring with a quantum dot coupled capacitively to a transmission line. In the presence of an Aharonov-Bohm flux this system exhibits a persistent current. This current is a measure of the coherence of the ground state. As a function of the coupling strength the ground state undergoes a crossover from a state characterized by a time-averaged persistent current which is much larger than its time-averaged mean squared fluctuations to a state characterized by a persistent current with an average amplitude that is much smaller than its mean squared fluctuations.
We investigate the effect of local charge detection in an Aharonov-Bohm ring composed of NNN identical coupled quantum dots. It is found that the single-electron persistent current of the ring is not fully suppressed in the limit of perfect charge detection except for the case of N=2N=2N=2. This property is analyzed for a single electron in the number-state representation. We point out that the nonvanishing persistent current can be understood in terms of the single-electron entanglement in the number-state representation. In addition, we find that the local charge detection may produce a finite persistent current even in the absence of the external magnetic fields.
We study the effect of electron-electron interaction on transport through a tunnel-coupled single-channel ring. We find that the conductance as a function of magnetic flux shows a series of interaction-induced resonances that survive thermal averaging. The period of the series is given by the interaction strength α. The physics behind this behavior is the blocking of the tunneling current by the circular current. The main mechanism of dephasing is due to circular-current fluctuations. The dephasing rate is proportional to the tunneling rate and does not depend on α.
In this thesis I find an analytic expression for the conductance of a single electron transistor in the regime when temperature, level spacing, and charging energy of an island are all of the same order. I also study the correction to the spacing between Coulomb blockade peaks due to finite dot-lead tunnel couplings. I find analytic expressions for both correction to the spacing averaged over mesoscopic fluctuations and the rms of the correction fluctuations. In the second part of the thesis I discuss the feasibility of quantum dot based spin- and charge-qubits. Firstly, I study the effect of mesoscopic fluctuations on the magnitude of errors that can occur in exchange operations on quantum dot spin-qubits. Mid-size double quantum dots, with an odd number of electrons in the range of a few tens in each dot, are investigated through the constant interaction model using realistic parameters. It is found that the number of independent parameters per dot that one should tune depends on the configuration and ranges from one to four. Then, I study decoherence of a quantum dot charge qubit due to coupling to piezoelectric acoustic phonons in the Born-Markov approximation. After including appropriate form factors, I find that phonon decoherence rates are one to two orders of magnitude weaker than was previously predicted. My results suggest that mechanisms other than phonon decoherence play a more significant role in current experimental setups.
Mesoscopic multiply connected samples such as conducting rings, cylinders or tori exhibit quantum size phenomena originating from the Aharonov–Bohm effects. One of the most spectacular phenomena is a persistent current [1] which is a direct manifestation of quantum phase coherence of the current carriers over a mesoscopic length scale. At a non-zero temperature, T > 0, the phase coherence of carriers is weakened and the samples exhibit the dissipative Ohmic contribution to the total current. There is a regime of temperatures in which both phase-coherent and dissipative Ohmic currents coexist. Such currents generate a magnetic flux. Its properties can be studied via modelling based on kinetic equations like Langevin equations [2]. The long-time, steady states of the magnetic flux are characterized by properties of the stationary probability density obtained from the corresponding Langevin equation. For instance, if the stationary probability density is bimodal, i.e., it has two maxima it reflects the possibility of occurrence of non-zero magnetic fluxes and in consequence the currents. One can notice an obvious analogy to the Josephson-based flux qubits [3]. There are serious advantages for using non-superconducting samples like rings as a building blocks for qubit storage because due to a small size they seem to be more stable with respect to decoherence and dephasing [4]. For higher temperatures, when __________
The time evolution of a qubit, consisting of two single-level quantum dots, is studied in the presence of telegraph noise. The dots are connected by two tunneling paths with an Aharonov-Bohm flux enclosed between them. Under special symmetry conditions, which can be achieved by tuning gate voltages, there develops partial decoherence: at long times, the off-diagonal element of the reduced density matrix (in the basis of the two dot states) approaches a nonzero value, generating a circulating current around the loop. The flux dependence of this current contains full information on the initial quantum state of the qubit, even at infinite time. Small deviations from this symmetry yield a very slow exponential decay toward the fully decoherent limit. However, the amplitudes of this decay also contain the full information on the initial qubit state, measurable either via the current or via the occupations of the qubit dots.