A quantum computer in the scheme of an atomic quantum transistor with logical encoding of qubits

A scheme of a multiqubit quantum computer on atomic ensembles using a quantum transistor implementing two qubit gates is proposed. We demonstrate how multiatomic ensembles permit one to work with a large number of qubits that are represented in a logical encoding in which each qubit is recorded on a superposition of single-particle states of two atomic ensembles. The access to qubits is implemented by appropriate phasing of quantum states of each of atomic ensembles. An atomic quantum transistor is proposed for use when executing two qubit operations. The quantum transistor effect appears when an excitation quantum is exchanged between two multiatomic ensembles located in two closely positioned QED cavities connected with each other by a gate atom. The dynamics of quantum transfer between atomic ensembles can be different depending on one of two states of the gate atom. Using the possibilities of control for of state of the gate atom, we show the possibility of quantum control for the state of atomic ensembles and, based on this, implementation of basic single and two qubit gates. Possible implementation schemes for a quantum computer on an atomic quantum transistor and their advantages in practical implementation are discussed.     

Localization in a quantum spin Hall system

The localization problem of electronic states in a two-dimensional quantum spin Hall system (that is, a symplectic ensemble with topological term) is studied by the transfer matrix method. The phase diagram in the plane of energy and disorder strength is exposed, and demonstrates "levitation" and "pair annihilation" of the domains of extended states analogous to that of the integer quantum Hall system. The critical exponent nu for the divergence of the localization length is estimated as nu congruent with 1.6, which is distinct from both exponents pertaining to the conventional symplectic and the unitary quantum Hall systems. Our analysis strongly suggests a different universality class related to the topology of the pertinent system.     

Interferometry with entangled atoms

A quantum gravity-gradiometer consists of two spatially separated ensembles of atoms interrogated by pulses of a common laser beam. The laser pulses cause the probability amplitudes of atomic ground-state hyperfine levels to interfere, producing two, motion-sensitive, phase shifts, which allow the measurement of the average acceleration of each ensemble, and, via simple differencing, of the acceleration gradient. Here we propose entangling the quantum states of atoms from the two ensembles prior to the pulse sequence, and show that entanglement encodes their relative acceleration in a single interference phase which can be measured directly, with no need for differencing. Received 6 June 2002 / Received in final form 25 October 2002 Published online 28 January 2003     

Phase diagram for quantum hall bilayers at nu=1

We present a phase diagram for a double quantum well bilayer electron gas in the quantum Hall regime at a total filling factor nu=1, based on exact numerical calculations of the topological Chern number matrix and the (interlayer) superfluid density. We find three phases: a quantized Hall state with pseudospin superfluidity, a quantized Hall state with pseudospin "gauge-glass" order, and a decoupled composite Fermi liquid. Comparison with experiments provides a consistent explanation of the observed quantum Hall plateau, Hall drag plateau, and vanishing Hall drag resistance, as well as the zero-bias conductance peak effect, and suggests some interesting points to pursue experimentally.     

Multiple phases with the same quantized Hall conductance in a two-subband system

In a two-dimensional electron system with two occupied subbands, the experimentally determined phase diagram in the density-magnetic field plane exhibits rich topological features. Ringlike structures are observed at even integer filling factors in the phase diagram. Even with the identical quantized Hall resistance values as those given by the ordinary integer quantum Hall effect due to the Landau level quantization, the activation energies of these states within the rings are much smaller. These ring structures cannot be accounted for by the simple single particle picture. We argue that ferromagnetic quantum Hall states, due to the interaction of two energy levels with opposite spin and different subband indices, are responsible for these unusual structures.     

A modern review of the two-level approximation

The paradigm of the two-level atom is revisited and its perturbative analysis is discussed in view of the principle of duality in perturbation theory. The models we consider are a two-level atom and an ensemble of two-level atoms both interacting with a single radiation mode. The aim is to see how the latter can be actually used as an amplifier of quantum fluctuations to the classical level through the thermodynamic limit of a very large ensemble of two-level atoms [M. Frasca, Phys. Lett. A 283 (2001) 271] and how can remove Schrödinger cat states. The thermodynamic limit can be very effective for producing both classical states and decoherence on a quantum system that evolves without dissipation. Decoherence without dissipation is indeed an effect of a single two-level atom interacting with an ensemble of two-level atoms, a situation that proves to be useful to understand recent experiments on nanoscale devices showing unexpected disappearance of quantum coherence at very low temperatures.     

Particle-hole symmetry and the Pfaffian state

We show that the particle-hole conjugate of the Pfaffian state-or "anti-Pfaffian" state-is in a different universality class from the Pfaffian state, with different topological order. The two states can be distinguished easily by their edge physics: their edges differ in both their thermal Hall conductance and their tunneling exponents. At the same time, the two states are exactly degenerate in energy for a nu=5/2 quantum Hall system in the idealized limit of zero Landau level mixing. Thus, both are good candidates for the observed sigma_{xy}=5/2(e;{2}/h) quantum Hall plateau.     

Hamiltonian Formulation of Statistical Ensembles and Mixed States of Quantum and Hybrid Systems

Representation of quantum states by statistical ensembles on the quantum phase space in the Hamiltonian form of quantum mechanics is analyzed. Various mathematical properties and some physical interpretations of the equivalence classes of ensembles representing a mixed quantum state in the Hamiltonian formulation are examined. In particular, non-uniqueness of the quantum phase space probability density associated with the quantum mixed state, Liouville dynamics of the probability densities and the possibility to represent the reduced states of bipartite systems by marginal distributions are discussed in detail. These considerations are used to study ensembles of hybrid quantum-classical systems. In particular, nonlinear evolution of a single hybrid system in a pure state and unequal evolutions of initially equivalent ensembles are discussed in the context of coupled hybrid systems.     

A Real Ensemble Interpretation of Quantum Mechanics

A new ensemble interpretation of quantum mechanics is proposed according to which the ensemble associated to a quantum state really exists: it is the ensemble of all the systems in the same quantum state in the universe. Individual systems within the ensemble have microscopic states, described by beables. The probabilities of quantum theory turn out to be just ordinary relative frequencies probabilities in these ensembles. Laws for the evolution of the beables of individual systems are given such that their ensemble relative frequencies evolve in a way that reproduces the predictions of quantum mechanics.     

Quantum Quenches with Random Matrix Hamiltonians and Disordered Potentials

We numerically investigate statistical ensembles for the occupations of eigenstates of an isolated quantum system emerging as a result of quantum quenches. The systems investigated are sparse random matrix Hamiltonians and disordered lattices. In the former case, the quench consists of sudden switching‐on the off‐diagonal elements of the Hamiltonian. In the latter case, it is sudden switching‐on of the hopping between adjacent lattice sites. The quench‐induced ensembles are compared with the so‐called “quantum micro‐canonical” (QMC) ensemble describing quantum superpositions with fixed energy expectation values. Our main finding is that quantum quenches with sparse random matrices having one special diagonal element lead to the condensation phenomenon predicted for the QMC ensemble. Away from the QMC condensation regime, the overall agreement with the QMC predictions is only qualitative for both random matrices and disordered lattices but with some cases of a very good quantitative agreement. In the case of disordered lattices, the QMC ensemble can be used to estimate the probability of finding a particle in a localized or delocalized eigenstate.     

Topological invariants for fractional quantum hall states

We calculate a topological invariant, whose value would coincide with the Chern number in the case of integer quantum Hall effect, for fractional quantum Hall states. In the case of Abelian fractional quantum Hall states, this invariant is shown to be equal to the trace of the K-matrix. In the case of non-Abelian fractional quantum Hall states, this invariant can be calculated on a case by case basis from the conformal field theory describing these states. This invariant can be used, for example, to distinguish between different fractional Hall states numerically even though, as a single number, it cannot uniquely label distinct states.     

Density Matrix in Quantum Mechanics and Distinctness of Ensembles Having the Same Compressed Density Matrix

We clarify different definitions of the density matrix by proposing the use of different names, the full density matrix for a single-closed quantum system, the compressed density matrix for the averaged single molecule state from an ensemble of molecules, and the reduced density matrix for a part of an entangled quantum system, respectively. We show that ensembles with the same compressed density matrix can be physically distinguished by observing fluctuations of various observables. This is in contrast to a general belief that ensembles with the same compressed density matrix are identical. Explicit expression for the fluctuation of an observable in a specified ensemble is given. We have discussed the nature of nuclear magnetic resonance quantum computing. We show that the conclusion that there is no quantum entanglement in the current nuclear magnetic resonance quantum computing experiment is based on the unjustified belief that ensembles having the same compressed density matrix are identical physically. Related issues in quantum communication are also discussed.     

Teleportation of an atomic ensemble quantum state

We propose a protocol to achieve high fidelity quantum state teleportation of a macroscopic atomic ensemble using a pair of quantum-correlated atomic ensembles. We show how to prepare this pair of ensembles using quasiperfect quantum state transfer processes between light and atoms. Our protocol relies on optical joint measurements of the atomic ensemble states and magnetic feedback reconstruction.     

Adiabatic Passage of Collective Excitations in Atomic Ensembles

We describe a theoretical scheme that allows for transfer of quantum states of atomic collective excitation between two macroscopic atomic ensembles localized in two spatially-separated domains. The conception is based on the occurrence of double-exciton dark states due to the collective destructive quantum interference of the emissions from the two atomic ensembles. With an adiabatically coherence manipulation for the atom-field couplings by stimulated Rmann scattering, the dark states will extrapolate from an exciton state of an ensemble to that of another. This realizes the transport of quantum information among atomic ensembles.     

声子晶体中的多重拓扑相

研究了圆环型波导依照蜂窝结构排列的声子晶体系统中的拓扑相变.利用晶格结构的点群对称性实现赝自旋,并在圆环中引入旋转气流来打破时间反演对称性.通过紧束缚近似模型计算的解析结果表明,没有引入气流时,调节几何参数,系统存在普通绝缘体和量子自旋霍尔效应绝缘体两个相;引入气流后,可以实现新的时间反演对称性破缺的量子自旋霍尔效应相,而增大气流强度,则可以实现量子反常霍尔效应相.这三个拓扑相可以通过自旋陈数来分类.通过有限元软件模拟了多个系统中边界态的传播,发现不同于量子自旋霍尔效应相,量子反常霍尔相系统的表面只支持一种自旋的边界态,并且它无需时间反演对称性保护.     

Adiabatic Passage of Collective Excitations in Atomic Ensembles

We describe a theoretical scheme that allows for transfer of quantum states of atomic collective excitation between two macroscopic atomic ensembles localized in two spatially-separated domains. The conception is based on the occurrence of double-exciton dark states due to the collective destructive quantum interference of the emissions from the two atomic ensembles. With an adiabatically coherence manipulation for the atom-field couplings by stimulated Ramann scattering, the dark states will extrapolate from an exciton state of an ensemble to that of another. This realizes the transport of quantum information among atomic ensembles.     

Hybrid quantum processors: molecular ensembles as quantum memory for solid state circuits

We investigate a hybrid quantum circuit where ensembles of cold polar molecules serve as long-lived quantum memories and optical interfaces for solid state quantum processors. The quantum memory realized by collective spin states (ensemble qubit) is coupled to a high-Q stripline cavity via microwave Raman processes. We show that, for convenient trap-surface distances of a few microm, strong coupling between the cavity and ensemble qubit can be achieved. We discuss basic quantum information protocols, including a swap from the cavity photon bus to the molecular quantum memory, and a deterministic two qubit gate. Finally, we investigate coherence properties of molecular ensemble quantum bits.