Nonadiabatic Geometric Phase and Induced Persistent Current in Mesoscopic Square Circuit with Tilted Magnetic Field at Edges

We investigate the geometric phase produced by nonadiabatic transition of spin states at corners of mesoscopic square circuit with tilted magnetic field at its edges, From the Schrodlnger equation, the transitions of electron spin state at corners are described by the transfer matrices. The eigenenergies and eigenstates are obtained from the cyclic condition and the multiplying of the transfer matrices. We show that there exist persistent charge and spin currents in such a system due to the lift of degeneracy between the opposite moving directions in the presence of the tilted magnetic field. The dependences of eigenenergies, geometric phase, charge and spin persistent currents on the tilting angles of magnetic field are analysed.     

Squeezing Effect of the Charge and Current in Mesoscopic Coupled Circuit with Alternating Source

We study the dynamic evolution of a mesoscopic coupled circuit with alternating source and solve its time-dependent Schrödinger equation with the help of the time dependent invariant of the Hermitian operator. It indicates that the state of the system can evolve a generalized squeezed state. The results show that in certain circumstance, compared to the initial vacuum state, either the charges or the currents in two meshes are squeezed simultaneously in the same extent. The expression of the nonadiabatic geometric phase in the circuit is also obtained.     

Linear response,persistent currents and related problems

Based on a general linear response approach we provide a systematic and unified survey of existing theories on persistent currents. The central notions in this context are equilibrium and dynamic persistent currents which are analyzed with respect to their similarities and differences in the canonical and grand canonical ensemble. We present criteria which relate the existence of persistent currents to the equipartition law and ergodicity for current correlators. We find that in additive Fermion systems at low temperatures both kinds of persistent currents coincide in the canonical ensemble whereas they differ in the grand canonical ensemble. Comparing different works on averaged persistent currents in diffusive mesoscopic rings within our framework and discussing several methods of calculating canonical currents with the help of grand canonical ensembles, we clarify some misunderstandings which have arisen in methodologically different approaches to the phenomenon of persistent currents. Finally, we relate the presence of dynamic persistent currents to the Hall conductivity on a finite cylinder and the center coordinate Kubo formula for the Hall conductivity.     

Implementation of universal quantum gates based on nonadiabatic geometric phases

We propose an experimentally feasible scheme to achieve quantum computation based on nonadiabatic geometric phase shifts, in which a cyclic geometric phase is used to realize a set of universal quantum gates. Physical implementation of this set of gates is designed for Josephson junctions and for NMR systems. Interestingly, we find that the nonadiabatic phase shift may be independent of the operation time under appropriate controllable conditions. A remarkable feature of the present nonadiabatic geometric gates is that there is no intrinsic limitation on the operation time.     

Optical clock with millihertz linewidth based on a phase-matching effect

We propose a new scheme for the optical frequency standard based on the phase-matching effect of the nonadiabatic interaction of two quasimonochromatic fields with the states 1S0, 1P1, and 3P0 of atoms 88Sr, which are trapped in an optical lattice with magic wavelength. After establishing the phase correlation between two laser fields by the nonadiabatic process, the final linewidth for the difference frequency field, which can be generated by a nonlinear optical crystal, is about 1 mHz.     

Nonadiabatic electron charge pumping in coupled semiconductor quantum dots

The possibility of nonadiabatic electron pumping in the system of three coupled quantum dots (QDs) attached to the leads is discussed. We have found out that periodical changing of energy level position in the middle QD results in non-zero mean tunneling current appeared due to nonadiabatic non-equilibrium processes. The same principle can be used for fabrication of a new class of semiconductor electronic devices based on non-stationary non-equilibrium currents. As an example we propose a nanometer quantum emitter with non-stationary inverse level occupation achieved by electron pumping.     

On the role of electron correlation and disorder on persistent currents in isolated one-dimensional rings

To understand the role of electron correlation and disorder on persistent currents in isolated 1D rings threaded by magnetic flux ?, we study the behavior of persistent currents in aperiodic and ordered binary alloy rings. These systems may be regarded as disordered systems with well-defined long-range order so that we do not have to perform any configuration averaging of the physical quantities. We see that in the absence of interaction, disorder suppresses persistent currents by orders of magnitude and also removes its discontinuity as a function of ?. As we introduce electron correlation, we get enhancement of the currents in certain disordered rings. Quite interestingly we observe that in some cases, electron correlation produces kink-like structures in the persistent current as a function of ?. This may be considered as anomalous Aharonov-Bohm oscillations of the persistent current and recent experimental observations support such oscillations. We find that the persistent current converges with the size of the rings.     

Persistent currents in a lattice correlated electron ring with a magnetic impurity

The behavior of charge and spin persistent currents in an integrable lattice ring of strongly correlated electrons with a magnetic impurity is exactly studied. Our results manifest that the oscillations of charge and spin persistent currents are similar to the ones, earlier obtained for integrable continuum models with a magnetic impurity. The difference is due to two (instead of one) Fermi velocities of low-lying excitations. The form of oscillations in the ground state is “saw-tooth”-like, generic for any multi-particle coherent one-dimensional models. The integrable magnetic impurity introduces net charge and spin chiralities in the generic integrable lattice system, which determine the initial phase shifts of charge and spin persistent currents. We show that the magnitude of the charge persistent current in the generic Kondo situation does not depend on the parameters of the magnetic impurity, unlike the (magneto)resistivity of transport currents. Received 30 January 2003 / Received in final form 12 March 2003 Published online 11 April 2003 RID="a" ID="a"e-mail: zvyagin@fy.chalmers.se     

Sweeping from the superfluid to the Mott phase in the Bose-Hubbard model

We study the sweep through the quantum phase transition from the superfluid to the Mott state for the Bose-Hubbard model with a time-dependent tunneling rate J(t). In the experimentally relevant case of exponential decay J(t) proportional variant e -gamma t, an adapted mean-field expansion for large fillings n yields a scaling solution for the fluctuations. This enables us to analytically calculate the evolution of the number and phase variations (on-site) and correlations (off-site) for slow (gammamu) sweeps, where mu is the chemical potential. Finally, we derive the dynamical decay of the off-diagonal long-range order as well as the temporal shrinkage of the superfluid fraction in a persistent ring-current setup.     

Polaronic and nonadiabatic phase diagram from anomalous isotope effects

Isotope effects (IEs) are powerful tools to probe directly the dependence of many physical properties on lattice dynamics. In this Letter we investigate the onset of anomalous IEs in the spinless Holstein model by employing the dynamical mean field theory. We show that the isotope coefficients of the electron effective mass and of the dressed phonon frequency are sizable also far away from the polaronic crossover and mark the importance of nonadiabatic lattice fluctuations. We draw a nonadiabatic phase diagram in which we identify a novel crossover, not related to polaronic features, where the IEs attain their largest anomalies.     

State-Independent Geometric Quantum Gates via Nonadiabatic and Noncyclic Evolution

Geometric phases are robust to local noises and the nonadiabatic ones can reduce the evolution time, thus nonadiabatic geometric gates have strong robustness and can approach high fidelity. However, the advantage of geometric phase has not been fully explored in previous investigations. Here,a scheme is proposed for universal quantum gates with pure nonadiabatic and noncyclic geometric phases from smooth evolution paths. In the scheme, only geometric phase can be accumulated in a fast way, and thus it not only fully utilizes the local noise resistant property of geometric phase but also reduces the difficulty in experimental realization. Numerical results show that the implemented geometric gates have stronger robustness than dynamical gates and the geometric scheme with cyclic path. Furthermore, it proposes to construct universal quantum gate on superconducting circuits, with the fidelities of single-qubit gate and nontrivial two-qubit gate can achieve 99.97% and 99.87%, respectively. Therefore, these high-fidelity quantum gates are promising for large-scale fault-tolerant quantum computation.     

Persistent current in a superconductor/quantum-dot ring/superconductor system

By means of the non-equilibrium Green's function technique, the inter-dot and Josephson currents in a superconductor/quantum-dot ring/superconductor (S/QDR/S) system are theoretically investigated. We found that a persistent current can coexist with the Josephson current in this hybrid QDR system when the inter-dot currents are all flowing in the clockwise (or anticlockwise) direction. The magnitude and direction of the persistent current can be controlled experimentally by the adjustment of some structure parameters, such as the quantum dot (QD) levels, the phase difference of the two external superconducting leads and the magnetic flux phase factor.     

Geometric phase and nonadiabatic effects in an electronic harmonic oscillator

Steering a quantum harmonic oscillator state along cyclic trajectories leads to a path-dependent geometric phase. Here we describe its experimental observation in an electronic harmonic oscillator. We use a superconducting qubit as a nonlinear probe of the phase, which is otherwise unobservable due to the linearity of the oscillator. We show that the geometric phase is, for a variety of cyclic paths, proportional to the area enclosed in the quadrature plane. At the transition to the nonadiabatic regime, we study corrections to the phase and dephasing of the qubit caused by qubit-resonator entanglement. In particular, we identify parameters for which this dephasing mechanism is negligible even in the nonadiabatic regime. The demonstrated controllability makes our system a versatile tool to study geometric phases in open quantum systems and to investigate their potential for quantum information processing.     

Nonadiabatic Geometric Phase in Composite Systems and Its Subsystem

We point out that the time-dependent gauge transformation technique may be effective in investigating the nonadiabatic geometric phase of a subsystem in a composite system. As an example, we consider two uniaxially coupled spin -1/2 particles with one of particles driven by rotating magnetic field. The influences of coupling and precession frequency of the magnetic field on geometric phase are also discussed in detail.     

Nonadiabatic Berry Phase of a Two-State System and Nonstationarity of Quantum States

The nonadiabatic Berry phases in the magnetic resonance under .various initial conditions are investigated and compared with ,the adiabatic Berry phase. The generaJ formalism for calculating the nonadiabatic Berry phase of a two-state system in terpls of the expansion of instantaneous energy eigenstates is presented. Some numerical calculations and discussions are made. The Berry phase of a two-statesystem under an impulsive interaction is addressed.     

Current control in periodically driven quantum dots using nonadiabatic double crossing

The purpose of this Letter is to propose a method for controlling electron currents on quantum dots driven by an oscillating electric field. The effects of nonadiabatic transition on time-averaged currents are theoretically studied in dot systems where energy levels exhibit a double crossing within one period of the driving field. The current is enhanced or suppressed as a result of the constructive or destructive interference between different transition paths at a double crossing. The current also depends on the number of dots because of the presence of dot-lead coupling.     

An angular frequency dependence on the Aharonov–Casher geometric phase

A quantum effect characterized by a dependence of the angular frequency associated with the confinement of a neutral particle to a quantum ring on the quantum numbers of the system and the Aharonov–Casher geometric phase is discussed. Then, it is shown that persistent spin currents can arise in a two-dimensional quantum ring in the presence of a Coulomb-type potential. A particular contribution to the persistent spin currents arises from the dependence of the angular frequency on the geometric quantum phase.     

Floquet states and geometrical phase of a multi-level system in cyclic evolution

We study the electronic states of a mesoscopic system whose Hamiltonian has a complicated static multi-level energy structure and undergoes periodic evolution in time. By using the Floquet theory, we derive the quasienergies, the Floquet states, and the geometrical phase. It is shown numerically that the geometrical phase is strongly dependent on the evolution circuits in the parameter space and on the evolution frequency of the varying Hamiltonian. In some cases the nonadiabatic geometric phases can exhibit chaotic behavior. We also show a trend of phase compensation in pairs of states which could restore the phase coherence if the pairing occurs.     

Aharonov-Casher effect and persistent spin currents in a Coulomb-type potential induced by Lorentz symmetry breaking effects

We investigate quantum effects on a nonrelativistic neutral particle with a permanent magnetic dipole moment that interacts with an electric field. This neutral particle is also under the influence of a background that breaks the Lorentz symmetry. We focus on the Lorentz symmetry violation background determined by a space-like vector field. Then, we show that the effects of the violation of Lorentz symmetry can yield an attractive Coulomb-type potential. Furthermore, we obtain the bound state solutions to the Schrödinger-Pauli equation and show that the spectrum of energy is a function of the Aharonov-Casher geometric quantum phase. Finally, we discuss the arising of persistent spin currents.     

Nonadiabatic noncyclic geometric phase and ensemble average spectrum of conductance in disordered mesoscopic rings with spin-orbit coupling

We generalize Yang's theory from the U(1) gauge field to the non-Abelian U(1)xSU(2)(spin) gauge field. Based on this generalization and taking into account the geometric Pancharatnam phase as well as an effective Aharonov-Bohm (AB) phase in nonadiabatic noncyclic transport, we calculate the ensemble average Fourier spectrum of the conductance in disordered mesoscopic rings connected to two leads. Our theory can explain the experimental results reported by Morpurgo et al. [Phys. Rev. Lett. 80, 1050 (1998)] more satisfactorily. We indicate that the observed splitting stems from the nonadiabatic noncyclic Pancharatnam phase and the effective AB phase, both being dependent on spin-orbit coupling.