2,037 research outputs found
Time-convolutionless master equation for quantum dots: Perturbative expansion to arbitrary order
The master equation describing the non-equilibrium dynamics of a quantum dot
coupled to metallic leads is considered. Employing a superoperator approach, we
derive an exact time-convolutionless master equation for the probabilities of
dot states, i.e., a time-convolutionless Pauli master equation. The generator
of this master equation is derived order by order in the hybridization between
dot and leads. Although the generator turns out to be closely related to the
T-matrix expressions for the transition rates, which are plagued by
divergences, in the time-convolutionless generator all divergences cancel order
by order. The time-convolutionless and T-matrix master equations are contrasted
to the Nakajima-Zwanzig version. The absence of divergences in the
Nakajima-Zwanzig master equation due to the nonexistence of secular reducible
contributions becomes rather transparent in our approach, which explicitly
projects out these contributions. We also show that the time-convolutionless
generator contains the generator of the Nakajima-Zwanzig master equation in the
Markov approximation plus corrections, which we make explicit. Furthermore, it
is shown that the stationary solutions of the time-convolutionless and the
Nakajima-Zwanzig master equations are identical. However, this identity neither
extends to perturbative expansions truncated at finite order nor to dynamical
solutions. We discuss the conditions under which the Nakajima-Zwanzig-Markov
master equation nevertheless yields good results.Comment: 13 pages + appendice
Excitation energy transfer: Study with non-Markovian dynamics
In this paper, we investigate the non-Markovian dynamics of a model to mimic
the excitation energy transfer (EET) between chromophores in photosynthesis
systems. The numerical path integral method is used. This method includes the
non-Markovian effects of the environmental affects and it does not need the
perturbation approximation in solving the dynamics of systems of interest. It
implies that the coherence helps the EET between chromophores through lasting
the transfer time rather than enhances the transfer rate of the EET. In
particular, the non-Markovian environment greatly increase the efficiency of
the EET in the photosynthesis systems.Comment: 5 pages, 5 figure
Decoherence in a superconducting flux qubit with a pi-junction
We consider the use of a pi-junction for flux qubits to realize degenerate
quantum levels without external magnetic field. On the basis of the
Caldeira-Leggett model, we derive an effective spin-Boson model, and study
decoherece of this type of qubits. We estimate the dephasing time by using
parameters from recent experiments of SIFS junctions, and show that high
critical current and large subgap resistance are required for the pi-junction
to realize a long coherent time.Comment: 5 pages, 2 figure
Circuit theory for decoherence in superconducting charge qubits
Based on a network graph analysis of the underlying circuit, a quantum theory
of arbitrary superconducting charge qubits is derived. Describing the
dissipative elements of the circuit with a Caldeira-Leggett model, we calculate
the decoherence and leakage rates of a charge qubit. The analysis includes
decoherence due to a dissipative circuit element such as a voltage source or
the quasiparticle resistances of the Josephson junctions in the circuit. The
theory presented here is dual to the quantum circuit theory for superconducting
flux qubits. In contrast to spin-boson models, the full Hilbert space structure
of the qubit and its coupling to the dissipative environment is taken into
account. Moreover, both self and mutual inductances of the circuit are fully
included.Comment: 8 pages, 3 figures; v2: published version; typo in Eq.(30) corrected,
minor changes, reference adde
Multiple-time correlation functions for non-Markovian interaction: Beyond the Quantum Regression Theorem
Multiple time correlation functions are found in the dynamical description of
different phenomena. They encode and describe the fluctuations of the dynamical
variables of a system. In this paper we formulate a theory of non-Markovian
multiple-time correlation functions (MTCF) for a wide class of systems. We
derive the dynamical equation of the {\it reduced propagator}, an object that
evolve state vectors of the system conditioned to the dynamics of its
environment, which is not necessarily at the vacuum state at the initial time.
Such reduced propagator is the essential piece to obtain multiple-time
correlation functions. An average over the different environmental histories of
the reduced propagator permits us to obtain the evolution equations of the
multiple-time correlation functions. We also study the evolution of MTCF within
the weak coupling limit and it is shown that the multiple-time correlation
function of some observables satisfy the Quantum Regression Theorem (QRT),
whereas other correlations do not. We set the conditions under which the
correlations satisfy the QRT. We illustrate the theory in two different cases;
first, solving an exact model for which the MTCF are explicitly given, and
second, presenting the results of a numerical integration for a system coupled
with a dissipative environment through a non-diagonal interaction.Comment: Submitted (04 Jul 04
Dephasing of a superconducting flux qubit
In order to gain a better understanding of the origin of decoherence in
superconducting flux qubits, we have measured the magnetic field dependence of
the characteristic energy relaxation time () and echo phase relaxation
time () near the optimal operating point of a flux qubit. We
have measured by means of the phase cycling method. At the
optimal point, we found the relation . This means
that the echo decay time is {\it limited by the energy relaxation} (
process). Moving away from the optimal point, we observe a {\it linear}
increase of the phase relaxation rate () with the applied
external magnetic flux. This behavior can be well explained by the influence of
magnetic flux noise with a spectrum on the qubit
Dynamics of quantum dissipation systems interacting with bosonic canonical bath: Hierarchical equations of motion approach
A nonperturbative theory is developed, aiming at an exact and efficient
evaluation of a general quantum system interacting with arbitrary bath
environment at any temperature and in the presence of arbitrary time-dependent
external fields. An exact hierarchical equations of motion formalism is
constructed on the basis of calculus-on-path-integral algorithm, via the
auxiliary influence generating functionals related to the interaction bath
correlation functions in a parametrization expansion form. The corresponding
continued-fraction Green's functions formalism for quantum dissipation is also
presented. Proposed further is the principle of residue correction, not just
for truncating the infinite hierarchy, but also for incorporating the small
residue dissipation that may arise from the practical difference between the
true and the parametrized bath correlation functions. The final
residue-corrected hierarchical equations of motion can therefore be used
practically for the evaluation of arbitrary dissipative quantum systems.Comment: 12 pages, submitted to PR
Quantum Smoluchowski equation: A systematic study
The strong friction regime at low temperatures is analyzed systematically
starting from the formally exact path integral expression for the reduced
dynamics. This quantum Smoluchowski regime allows for a type of semiclassical
treatment in the inverse friction strength so that higher order quantum
corrections to the original quantum Smoluchowski equation [PRL 87, 086802
(2001), PRL 101, 11903 (2008)] can be derived. Drift and diffusion coefficients
are determined by the equilibrium distribution in position and are directly
related to the corresponding action of extremal paths and fluctuations around
them. It is shown that the inclusion of higher order corrections reproduces the
quantum enhancement above crossover for the decay rate out of a metastable well
exactly.Comment: 15 pages, 4 figure
Non-additivity of decoherence rates in superconducting qubits
We show that the relaxation and decoherence rates 1/T_1 and 1/T_2 of a qubit
coupled to several noise sources are in general not additive, i.e., that the
total rates are not the sums of the rates due to each individual noise source.
To demonstrate this, we calculate the relaxation and pure dephasing rates 1/T_1
and 1/T_\phi of a superconducting (SC) flux qubit in the Born-Markov
approximation in the presence of several circuit impedances Z_i using network
graph theory and determine their deviation from additivity (the mixing term).
We find that there is no mixing term in 1/T_\phi and that the mixing terms in
1/T_1 and 1/T_2 can be positive or negative, leading to reduced or enhanced
relaxation and decoherence times T_1 and T_2. The mixing term due to the
circuit inductance L at the qubit transition frequency \omega_{01} is generally
of second order in \omega_{01}L/Z_i, but of third order if all impedances Z_i
are pure resistances. We calculate T_{1,2} for an example of a SC flux qubit
coupled to two impedances.Comment: 5 pages, 2 figure
- …