arXiv:cond-mat/0702296 · Journal of Applied Physics

Decoherence processes of a quantum two-level system coupled to a fermionic environment

Naoyoshi Yamada, Akimasa Sakuma, Hiroki Tsuchiura

Published May 1, 2007• 8 citations

Abstract

We study decoherence processes of an S=1∕2 localized spin coupled to conduction band electrons in a metal or a semiconductor via an Ising-like interaction. We derive master equations for the density matrix of the localized spin by tracing out all degrees of freedom in the conduction electron system based on the linked-cluster-expansion technique. It is found that the decoherence occurs more rapidly for the metallic case than for semiconducting case.

DOI: 10.1063/1.2712944

Related papers

Conduction electrons and the decoherence of impurity-bound electrons in a semiconductor

Kuljit S. Virk, John E. Sipe

Physical Review BOct 18, 20057 citations

Conduction electrons and the decoherence of solid state qubits

Kuljit S. Virk, John E. Sipe

arXiv:cond-mat/0502629Feb 26, 20050 citations

Spin density matrix of a two-electron system. I. General theory and exact master equations

Sharif D. Kunikeev, Daniel A. Lidar

arXiv:0708.0644Physical Review BJan 17, 20081 citation

Quantum Decoherence and Weak Localization at Low Temperatures

Dmitry S. Golubev, Andrei D. Zaikin

arXiv:cond-mat/9712203Dec 17, 19970 citations

Dissipative quantum dynamics of fermions in optical lattices: A slave-spin approach

Jean-Sébastien Bernier, Dario Poletti, Corinna Kollath

arXiv:1407.1098Physical Review BNov 18, 201416 citations

Decoherence induced by interacting quantum spin baths

Davide Rossini, Tommaso Calarco, Vittorio Giovannetti +2 more

arXiv:quant-ph/0611242Physical Review AMar 26, 2007199 citations

arXiv:cond-mat/0702296 · Journal of Applied Physics

Decoherence processes of a quantum two-level system coupled to a fermionic environment

Naoyoshi Yamada, Akimasa Sakuma, Hiroki Tsuchiura

Published May 1, 2007• 8 citations

arXiv HTML PDF

Abstract

DOI: 10.1063/1.2712944

Related papers

Conduction electrons and the decoherence of impurity-bound electrons in a semiconductor

Kuljit S. Virk, John E. Sipe

We study the dynamics of impurity-bound electrons interacting with a bath of conduction band electrons in a semiconductor. Only the exchange interaction is considered. We derive master equations for the density matrices of single- and two-qubit systems under the usual Born and Markov approximations. The bath mediated Ruderman-Kittel-Kasuya-Yoshida interaction in the two-qubit case arises naturally. It leads to an energy shift significant only when the ratio $({R}_{T})$ of the interqubit distance to the thermal de Broglie wavelength of the bath electrons is small. This bath mediated interaction also has a profound impact on the decoherence times; the effect decreases monotonically with ${R}_{T}$ .We study the dynamics of impurity-bound electrons interacting with a bath of conduction band electrons in a semiconductor. Only the exchange interaction is considered. We derive master equations for the density matrices of single- and two-qubit systems under the usual Born and Markov approximations. The bath mediated Ruderman-Kittel-Kasuya-Yoshida interaction in the two-qubit case arises naturally. It leads to an energy shift significant only when the ratio $({R}_{T})$ of the interqubit distance to the thermal de Broglie wavelength of the bath electrons is small. This bath mediated interaction also has a profound impact on the decoherence times; the effect decreases monotonically with ${R}_{T}$.

Physical Review BOct 18, 20057 citations

Conduction electrons and the decoherence of solid state qubits

Kuljit S. Virk, John E. Sipe

We study the dynamics of impurity bound electrons interacting with a bath of conduction band electrons in a semiconductor. Only the exchange interaction is considered. We derive master equations for the density matrices of single and two qubit systems under the usual Born and Markov approximations. The bath mediated RKKY interaction in the two qubit case arises naturally. It leads to an energy shift significant only when the ratio ( $R_{T}$ ) of the inter-qubit distance to the thermal deBroglie wavelength of the bath electrons is small. This bath mediated interaction also has a profound impact on the decoherence times; the effect decreases monotonically with $R_{T}$ .We study the dynamics of impurity bound electrons interacting with a bath of conduction band electrons in a semiconductor. Only the exchange interaction is considered. We derive master equations for the density matrices of single and two qubit systems under the usual Born and Markov approximations. The bath mediated RKKY interaction in the two qubit case arises naturally. It leads to an energy shift significant only when the ratio ($R_{T}$) of the inter-qubit distance to the thermal deBroglie wavelength of the bath electrons is small. This bath mediated interaction also has a profound impact on the decoherence times; the effect decreases monotonically with $R_{T}$.

arXiv:cond-mat/0502629Feb 26, 20050 citations

Spin density matrix of a two-electron system. I. General theory and exact master equations

Sharif D. Kunikeev, Daniel A. Lidar

We consider a scenario where interacting electrons confined in quantum dots (QDs) are either too close to be resolved, or we do not wish to apply measurements that resolve them. Then, the physical observable is an electron spin only and the system state is fully described by the spin density matrix. Accounting for the spatial degrees of freedom, we examine to what extent a Hamiltonian description of the spin-only degrees of freedom is valid. We show that as long as there is no coupling between singlet and triplet states, this is indeed the case, but when there is such a coupling, there are open systems effects, i.e., the dynamics is nonunitary even without interaction with a true bath. Our primary focus is an investigation of nonunitary effects, based on exact master equations we derive for the spin density matrix in the Lindblad and time-convolutionless forms, and the implications for quantum computation. In particular, we demonstrate that the Heisenberg interaction does not affect the unitary part (apart from a Lamb shift) but does affect the nonunitary contributions to the time evolution of the spin density matrix. In a sequel paper, we present a detailed analysis of an example system of two quantum dots, including spin-orbit effects.We consider a scenario where interacting electrons confined in quantum dots (QDs) are either too close to be resolved, or we do not wish to apply measurements that resolve them. Then, the physical observable is an electron spin only and the system state is fully described by the spin density matrix. Accounting for the spatial degrees of freedom, we examine to what extent a Hamiltonian description of the spin-only degrees of freedom is valid. We show that as long as there is no coupling between singlet and triplet states, this is indeed the case, but when there is such a coupling, there are open systems effects, i.e., the dynamics is nonunitary even without interaction with a true bath. Our primary focus is an investigation of nonunitary effects, based on exact master equations we derive for the spin density matrix in the Lindblad and time-convolutionless forms, and the implications for quantum computation. In particular, we demonstrate that the Heisenberg interaction does not affect the unitary part (apart from a Lamb shift) but does affect the nonunitary contributions to the time evolution of the spin density matrix. In a sequel paper, we present a detailed analysis of an example system of two quantum dots, including spin-orbit effects.

arXiv:0708.0644Physical Review BJan 17, 20081 citation

Quantum Decoherence and Weak Localization at Low Temperatures

Dmitry S. Golubev, Andrei D. Zaikin

We develope a theory of a fundamental effect of the interaction-induced decoherence of the electron wave function in a disordered metal. With the aid of the Keldysh technique and the path integral formalism we derive a formally exact equation of motion for the electron density matrix in the presence of interaction. We demonstrate that the effect of interaction of the electron with other electrons and lattice ions in a disordered metal is equivalent to that of an effective dissipative environment. Quantum noise of this environment causes quantum decoherence even at T=0. Our analysis explicitely accounts for the Pauli principle which plays an important role for inelastic scattering processes but turns out not to affect quantum decoherence. Our results seriously challenge the existence of strong localization in low dimensional disordered metals.We develope a theory of a fundamental effect of the interaction-induced decoherence of the electron wave function in a disordered metal. With the aid of the Keldysh technique and the path integral formalism we derive a formally exact equation of motion for the electron density matrix in the presence of interaction. We demonstrate that the effect of interaction of the electron with other electrons and lattice ions in a disordered metal is equivalent to that of an effective dissipative environment. Quantum noise of this environment causes quantum decoherence even at T=0. Our analysis explicitely accounts for the Pauli principle which plays an important role for inelastic scattering processes but turns out not to affect quantum decoherence. Our results seriously challenge the existence of strong localization in low dimensional disordered metals.

arXiv:cond-mat/9712203Dec 17, 19970 citations

Dissipative quantum dynamics of fermions in optical lattices: A slave-spin approach

Jean-Sébastien Bernier, Dario Poletti, Corinna Kollath

We investigate the influence of a Markovian environment on the dynamics of interacting spinful fermionic atoms in a lattice. To explore the physical phenomena occurring at short times, we develop a method based on a slave-spin representation of fermions that is amenable to the investigation of the dynamics of dissipative systems. We apply this approach to two different dissipative couplings that can occur in current experiments: a coupling via the local density and a coupling via the local double occupancy. We complement our study based on this method, with results obtained using the adiabatic elimination technique and with an exact study of a two-site model. We uncover that the decoherence is slowed down by increasing either the interaction strength or the dissipative coupling (the Zeno effect). We also find, for the coupling to the local double occupancy, that the final steady state can sustain single-particle coherence.We investigate the influence of a Markovian environment on the dynamics of interacting spinful fermionic atoms in a lattice. To explore the physical phenomena occurring at short times, we develop a method based on a slave-spin representation of fermions that is amenable to the investigation of the dynamics of dissipative systems. We apply this approach to two different dissipative couplings that can occur in current experiments: a coupling via the local density and a coupling via the local double occupancy. We complement our study based on this method, with results obtained using the adiabatic elimination technique and with an exact study of a two-site model. We uncover that the decoherence is slowed down by increasing either the interaction strength or the dissipative coupling (the Zeno effect). We also find, for the coupling to the local double occupancy, that the final steady state can sustain single-particle coherence.

arXiv:1407.1098Physical Review BNov 18, 201416 citations

Decoherence induced by interacting quantum spin baths

Davide Rossini, Tommaso Calarco, Vittorio Giovannetti +2 more

We study decoherence induced on a two-level system coupled to a one-dimensional quantum spin chain. We consider the cases where the dynamics of the chain is determined by the Ising, $XY$ , or Heisenberg exchange Hamiltonian. This model of quantum baths can be of fundamental importance for the understanding of decoherence in open quantum systems, since it can be experimentally engineered by using atoms in optical lattices. As an example, here we show how to implement a pure dephasing model for a qubit system coupled to an interacting spin bath. We provide results that go beyond the case of a central spin coupled uniformly to all the spins of the bath, in particular showing what happens when the bath enters different phases, or becomes critical; we also study the dependence of the coherence loss on the number of bath spins to which the system is coupled and we describe a coupling-independent regime in which decoherence exhibits universal features, irrespective of the system-environment coupling strength. Finally, we establish a relation between decoherence and entanglement inside the bath. For the Ising and the $XY$ models we are able to give an exact expression for the decay of coherences, while for the Heisenberg bath we resort to the numerical time-dependent density matrix renormalization group.We study decoherence induced on a two-level system coupled to a one-dimensional quantum spin chain. We consider the cases where the dynamics of the chain is determined by the Ising, $XY$, or Heisenberg exchange Hamiltonian. This model of quantum baths can be of fundamental importance for the understanding of decoherence in open quantum systems, since it can be experimentally engineered by using atoms in optical lattices. As an example, here we show how to implement a pure dephasing model for a qubit system coupled to an interacting spin bath. We provide results that go beyond the case of a central spin coupled uniformly to all the spins of the bath, in particular showing what happens when the bath enters different phases, or becomes critical; we also study the dependence of the coherence loss on the number of bath spins to which the system is coupled and we describe a coupling-independent regime in which decoherence exhibits universal features, irrespective of the system-environment coupling strength. Finally, we establish a relation between decoherence and entanglement inside the bath. For the Ising and the $XY$ models we are able to give an exact expression for the decay of coherences, while for the Heisenberg bath we resort to the numerical time-dependent density matrix renormalization group.

arXiv:quant-ph/0611242Physical Review AMar 26, 2007199 citations

({R}_{T})

of the interqubit distance to the thermal de Broglie wavelength of the bath electrons is small. This bath mediated interaction also has a profound impact on the decoherence times; the effect decreases monotonically with

{R}_{T}

R_{T}

) of the inter-qubit distance to the thermal deBroglie wavelength of the bath electrons is small. This bath mediated interaction also has a profound impact on the decoherence times; the effect decreases monotonically with

R_{T}

We study decoherence induced on a two-level system coupled to a one-dimensional quantum spin chain. We consider the cases where the dynamics of the chain is determined by the Ising,

XY

, or Heisenberg exchange Hamiltonian. This model of quantum baths can be of fundamental importance for the understanding of decoherence in open quantum systems, since it can be experimentally engineered by using atoms in optical lattices. As an example, here we show how to implement a pure dephasing model for a qubit system coupled to an interacting spin bath. We provide results that go beyond the case of a central spin coupled uniformly to all the spins of the bath, in particular showing what happens when the bath enters different phases, or becomes critical; we also study the dependence of the coherence loss on the number of bath spins to which the system is coupled and we describe a coupling-independent regime in which decoherence exhibits universal features, irrespective of the system-environment coupling strength. Finally, we establish a relation between decoherence and entanglement inside the bath. For the Ising and the

XY

models we are able to give an exact expression for the decay of coherences, while for the Heisenberg bath we resort to the numerical time-dependent density matrix renormalization group.