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Stub model for dephasing in a quantum dot

C. W. J. Beenakker, B. Michaelis

Published Jan 1, 2005• 8 citations
OpenAlex

Abstract

Abstract. As an alternative to Büttiker’s dephasing lead model, we examine a dephasing stub. Both models are phenomenological ways to introduce decoherence in chaotic scattering by a quantum dot. The difference is that the dephasing lead opens up the quantum dot by connecting it to an electron reservoir, while the dephasing stub is closed at one end. Voltage fluctuations in the stub take over the dephasing role from the reservoir. Because the quantum dot with dephasing lead is an open system, only expectation values of the current can be forced to vanish at low frequencies, while the outcome of an individual measurement is not so constrained. The quantum dot with dephasing stub, in contrast, remains a closed system with a vanishing low-frequency current at each and every measurement. This difference is a crucial one in the context of quantum algorithms, which are based on the outcome of individual measurements rather than on expectation values. We demonstrate that the dephasing stub model has a parameter range in which the voltage fluctuations are sufficiently strong to suppress quantum interference effects, while still being sufficiently weak that classical current fluctuations can be neglected relative to the nonequilibrium shot noise.

Related papers

Stub model for dephasing in a quantum dot

C. W. J. Beenakker, B Michaelis

As an alternative to Büttiker's dephasing lead model, we examine a dephasing stub . Both models are phenomenological ways to introduce decoherence in chaotic scattering by a quantum dot. The difference is that the dephasing lead opens up the quantum dot by connecting it to an electron reservoir, while the dephasing stub is closed at one end. Voltage fluctuations in the stub take over the dephasing role from the reservoir. Because the quantum dot with dephasing lead is an open system, only expectation values of the current can be forced to vanish at low frequencies, while the outcome of an individual measurement is not so constrained. The quantum dot with dephasing stub, in contrast, remains a closed system with a vanishing low-frequency current at each and every measurement. This difference is a crucial one in the context of quantum algorithms, which are based on the outcome of individual measurements rather than on expectation values. We demonstrate that the dephasing stub model has a parameter range in which the voltage fluctuations are sufficiently strong to suppress quantum interference effects, while still being sufficiently weak that classical current fluctuations can be neglected relative to the nonequilibrium shot noise.

arXiv:cond-mat/0503347•Journal of Physics A Mathematical and General•Nov 22, 2005•10 citations

Dephasing in quantum chaotic transport: A semiclassical approach

Robert S. Whitney, Philippe Jacquod, Cyril Petitjean

We investigate the effect of dephasing (decoherence) on quantum transport through open chaotic ballistic conductors in the semiclassical limit of small Fermi wavelength to system size ratio, ${\ensuremath{\lambda}}_{F}∕L⪡1$. We use the trajectory-based semiclassical theory to study a two-terminal chaotic dot with decoherence originating from (i) an external closed quantum chaotic environment, (ii) a classical source of noise, and (iii) a voltage probe, i.e., an additional current-conserving terminal. We focus on the pure dephasing regime, where the coupling to the external source of dephasing is so weak that it does not induce energy relaxation. In addition to the universal algebraic suppression of weak localization, we find an exponential suppression of weak localization $\ensuremath{\propto}\mathrm{exp}[\ensuremath{-}\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\tau}}∕{\ensuremath{\tau}}_{\ensuremath{\phi}}]$, with the dephasing rate ${\ensuremath{\tau}}_{\ensuremath{\phi}}^{\ensuremath{-}1}$. The parameter $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\tau}}$ depends strongly on the source of dephasing. For a voltage probe, $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\tau}}$ is of order the Ehrenfest time $\ensuremath{\propto}\mathrm{ln}[L∕{\ensuremath{\lambda}}_{F}]$. In contrast, for a chaotic environment or a classical source of noise, it has the correlation length $\ensuremath{\xi}$ of the coupling or noise potential replacing the Fermi wavelength ${\ensuremath{\lambda}}_{F}$. We explicitly show that the Fano factor for shot noise is unaffected by decoherence. We connect these results to earlier works on dephasing due to electron-electron interactions and numerically confirm our findings.

arXiv:0710.5137•Physical Review B•Jan 15, 2008•24 citations

Antiresonances as precursors of decoherence

Luis E. F. Foa Torres, Horacio M. Pastawski, Ernesto A. Medina

We show that, in the presence of a complex spectrum, antiresonances act as a precursor for dephasing enabling the crossover to a fully decoherent transport even within a unitary Hamiltonian description. This general scenario is illustrated here by focusing on a quantum dot coupled to a chaotic cavity containing a finite, but large, number of states using a Hamiltonian formulation. For weak coupling to a chaotic cavity with a sufficiently dense spectrum, the ensuing complex structure of resonances and antiresonances leads to phase randomization under coarse graining in energy. Such phase instabilities and coarse graining are the ingredients for a mechanism producing decoherence and thus irreversibility. For the present simple model one finds a conductance that coincides with the one obtained by adding a ficticious voltage probe within the Landauer-Büttiker picture. This sheds new light on how the microscopic mechanisms that produce phase fluctuations induce decoherence.

•Jan 1, 2006•19 citations

Dephasing due to background charge fluctuations

Toshifumi Itakura, 康弘 都倉

In quantum computation, quantum coherence must be maintained during gate operation. However, in physical implementations, various couplings with the environment are unavoidable and can lead to a dephasing of a quantum bit (qubit). The background charge fluctuations are an important dephasing process, especially in a charge qubit system. We examined the dephasing rate of a qubit due to random telegraph noise. Solving stochastic differential equations, we obtained the dephasing rate of a qubit constructed of a coupled-dot system; we applied our results to the charge Josephson qubit system. We examined the dephasing rates due to two types of couplings between the coupled-dot system and the background charge, namely, fluctuation in the tunnel coupling constant and fluctuation in the asymmetric bias. For a strong-coupling condition, the dephasing rate was inversely proportional to the time constant of the telegraph noise. When there is fluctuation in the tunnel coupling constant, Gaussian decay occurs in the initial regime. We also examined the rate of dephasing due to many impurity sites. For a weak-coupling condition with fluctuation in the asymmetric bias, the obtained dephasing rate coincided with that obtained by the perturbation method using the spectral weight of a boson thermal bath, which is proportional to the inverse of the frequency.

arXiv:cond-mat/0303412•Physical review. B, Condensed matter•May 16, 2003•91 citations

Antiresonances as precursors of decoherence

L. E. F. Foa Torres, H. M Pastawski, Ernesto A. Medina

We show that, in the presence of a complex spectrum, antiresonances act as a precursor for dephasing enabling the crossover to a fully decoherent transport even within a unitary Hamiltonian description. This general scenario is illustrated here by focusing on a quantum dot coupled to a chaotic cavity containing a finite, but large, number of states using a Hamiltonian formulation. For weak coupling to a chaotic cavity with a sufficiently dense spectrum, the ensuing complex structure of resonances and antiresonances leads to phase randomization under coarse graining in energy. Such phase instabilities and coarse graining are the ingredients for a mechanism producing decoherence and thus irreversibility. For the present simple model one finds a conductance that coincides with the one obtained by adding a ficticious voltage probe within the Landauer-Büttiker picture. This sheds new light on how the microscopic mechanisms that produce phase fluctuations induce decoherence.

arXiv:cond-mat/0511360•Europhysics Letters (EPL)•Dec 6, 2005•27 citations

Controlled Dephasing and Measurement Efficiency via Quantum Dot Detector

Gyong Luck Khym, Youngnae Lee, Kicheon Kang

We study charge detection and controlled dephasing of a mesoscopic system via a quantum dot detector (QDD), where the mesoscopic system and the QDD are capacitively coupled. The QDD is considered to have coherent resonant tunnelling via a single level. It is found that the dephasing rate is proportional to the square of the conductance of the QDD for the Breit-Wigner model, showing that the dephasing is completely different from the shot noise of the detector. The measurement rate, on the other hand, shows a dip near the resonance. Our findings are peculiar especially for a symmetric detector in the following aspect: The dephasing rate is maximum at resonance of the QDD where the detector conductance is insensitive to the charge state of the mesoscopic system. As a result, the efficiency of the detector shows a dip and vanishes at resonance, in contrast to the single-channel symmetric non-resonant detector that has always a maximum efficiency. We find that this difference originates from a very general property of the scattering matrix: The abrupt phase change exists in the scattering amplitudes in the presence of the symmetry, which is insensitive to the detector current but {\em stores} the information of the quantum state of the mesoscopic system.

arXiv:cond-mat/0601535•Journal of the Physical Society of Japan•Jun 8, 2006•10 citations
Abstract. As an alternative to Büttiker’s dephasing lead model, we examine a dephasing stub. Both models are phenomenological ways to introduce decoherence in chaotic scattering by a quantum dot. The difference is that the dephasing lead opens up the quantum dot by connecting it to an electron reservoir, while the dephasing stub is closed at one end. Voltage fluctuations in the stub take over the dephasing role from the reservoir. Because the quantum dot with dephasing lead is an open system, only expectation values of the current can be forced to vanish at low frequencies, while the outcome of an individual measurement is not so constrained. The quantum dot with dephasing stub, in contrast, remains a closed system with a vanishing low-frequency current at each and every measurement. This difference is a crucial one in the context of quantum algorithms, which are based on the outcome of individual measurements rather than on expectation values. We demonstrate that the dephasing stub model has a parameter range in which the voltage fluctuations are sufficiently strong to suppress quantum interference effects, while still being sufficiently weak that classical current fluctuations can be neglected relative to the nonequilibrium shot noise.
As an alternative to Büttiker's dephasing lead model, we examine a dephasing stub . Both models are phenomenological ways to introduce decoherence in chaotic scattering by a quantum dot. The difference is that the dephasing lead opens up the quantum dot by connecting it to an electron reservoir, while the dephasing stub is closed at one end. Voltage fluctuations in the stub take over the dephasing role from the reservoir. Because the quantum dot with dephasing lead is an open system, only expectation values of the current can be forced to vanish at low frequencies, while the outcome of an individual measurement is not so constrained. The quantum dot with dephasing stub, in contrast, remains a closed system with a vanishing low-frequency current at each and every measurement. This difference is a crucial one in the context of quantum algorithms, which are based on the outcome of individual measurements rather than on expectation values. We demonstrate that the dephasing stub model has a parameter range in which the voltage fluctuations are sufficiently strong to suppress quantum interference effects, while still being sufficiently weak that classical current fluctuations can be neglected relative to the nonequilibrium shot noise.
We investigate the effect of dephasing (decoherence) on quantum transport through open chaotic ballistic conductors in the semiclassical limit of small Fermi wavelength to system size ratio, ${\ensuremath{\lambda}}_{F}∕L⪡1$. We use the trajectory-based semiclassical theory to study a two-terminal chaotic dot with decoherence originating from (i) an external closed quantum chaotic environment, (ii) a classical source of noise, and (iii) a voltage probe, i.e., an additional current-conserving terminal. We focus on the pure dephasing regime, where the coupling to the external source of dephasing is so weak that it does not induce energy relaxation. In addition to the universal algebraic suppression of weak localization, we find an exponential suppression of weak localization $\ensuremath{\propto}\mathrm{exp}[\ensuremath{-}\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\tau}}∕{\ensuremath{\tau}}_{\ensuremath{\phi}}]$, with the dephasing rate ${\ensuremath{\tau}}_{\ensuremath{\phi}}^{\ensuremath{-}1}$. The parameter $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\tau}}$ depends strongly on the source of dephasing. For a voltage probe, $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\tau}}$ is of order the Ehrenfest time $\ensuremath{\propto}\mathrm{ln}[L∕{\ensuremath{\lambda}}_{F}]$. In contrast, for a chaotic environment or a classical source of noise, it has the correlation length $\ensuremath{\xi}$ of the coupling or noise potential replacing the Fermi wavelength ${\ensuremath{\lambda}}_{F}$. We explicitly show that the Fano factor for shot noise is unaffected by decoherence. We connect these results to earlier works on dephasing due to electron-electron interactions and numerically confirm our findings.
We show that, in the presence of a complex spectrum, antiresonances act as a precursor for dephasing enabling the crossover to a fully decoherent transport even within a unitary Hamiltonian description. This general scenario is illustrated here by focusing on a quantum dot coupled to a chaotic cavity containing a finite, but large, number of states using a Hamiltonian formulation. For weak coupling to a chaotic cavity with a sufficiently dense spectrum, the ensuing complex structure of resonances and antiresonances leads to phase randomization under coarse graining in energy. Such phase instabilities and coarse graining are the ingredients for a mechanism producing decoherence and thus irreversibility. For the present simple model one finds a conductance that coincides with the one obtained by adding a ficticious voltage probe within the Landauer-Büttiker picture. This sheds new light on how the microscopic mechanisms that produce phase fluctuations induce decoherence.
In quantum computation, quantum coherence must be maintained during gate operation. However, in physical implementations, various couplings with the environment are unavoidable and can lead to a dephasing of a quantum bit (qubit). The background charge fluctuations are an important dephasing process, especially in a charge qubit system. We examined the dephasing rate of a qubit due to random telegraph noise. Solving stochastic differential equations, we obtained the dephasing rate of a qubit constructed of a coupled-dot system; we applied our results to the charge Josephson qubit system. We examined the dephasing rates due to two types of couplings between the coupled-dot system and the background charge, namely, fluctuation in the tunnel coupling constant and fluctuation in the asymmetric bias. For a strong-coupling condition, the dephasing rate was inversely proportional to the time constant of the telegraph noise. When there is fluctuation in the tunnel coupling constant, Gaussian decay occurs in the initial regime. We also examined the rate of dephasing due to many impurity sites. For a weak-coupling condition with fluctuation in the asymmetric bias, the obtained dephasing rate coincided with that obtained by the perturbation method using the spectral weight of a boson thermal bath, which is proportional to the inverse of the frequency.
We show that, in the presence of a complex spectrum, antiresonances act as a precursor for dephasing enabling the crossover to a fully decoherent transport even within a unitary Hamiltonian description. This general scenario is illustrated here by focusing on a quantum dot coupled to a chaotic cavity containing a finite, but large, number of states using a Hamiltonian formulation. For weak coupling to a chaotic cavity with a sufficiently dense spectrum, the ensuing complex structure of resonances and antiresonances leads to phase randomization under coarse graining in energy. Such phase instabilities and coarse graining are the ingredients for a mechanism producing decoherence and thus irreversibility. For the present simple model one finds a conductance that coincides with the one obtained by adding a ficticious voltage probe within the Landauer-Büttiker picture. This sheds new light on how the microscopic mechanisms that produce phase fluctuations induce decoherence.
We study charge detection and controlled dephasing of a mesoscopic system via a quantum dot detector (QDD), where the mesoscopic system and the QDD are capacitively coupled. The QDD is considered to have coherent resonant tunnelling via a single level. It is found that the dephasing rate is proportional to the square of the conductance of the QDD for the Breit-Wigner model, showing that the dephasing is completely different from the shot noise of the detector. The measurement rate, on the other hand, shows a dip near the resonance. Our findings are peculiar especially for a symmetric detector in the following aspect: The dephasing rate is maximum at resonance of the QDD where the detector conductance is insensitive to the charge state of the mesoscopic system. As a result, the efficiency of the detector shows a dip and vanishes at resonance, in contrast to the single-channel symmetric non-resonant detector that has always a maximum efficiency. We find that this difference originates from a very general property of the scattering matrix: The abrupt phase change exists in the scattering amplitudes in the presence of the symmetry, which is insensitive to the detector current but {\em stores} the information of the quantum state of the mesoscopic system.