Optical selection rules and phase-dependent adiabatic state control in a superconducting quantum circuit

We analyze the optical selection rules of the microwave-assisted transitions in a flux qubit superconducting quantum circuit (SQC). We show that the parities of the states relevant to the superconducting phase in the SQC are well defined when the external magnetic flux phi(e) = phi(0)/2; then the selection rules are the same as the ones for the electric-dipole transitions in usual atoms. When phi(e) does not = phi(0)/2, the symmetry of the potential of the artificial "atom" is broken, a so-called delta-type "cyclic" three-level atom is formed, where one- and two-photon processes can coexist. We study how the population of these three states can be selectively transferred by adiabatically controlling the electromagnetic field pulses. Different from lambda-type atoms, the adiabatic population transfer in our three-level delta atom can be controlled not only by the amplitudes but also by the phases of the pluses.     

The quasiclassical Langevin equation and its application to the decay of a metastable state and to quantum fluctuations

We report on investigations on the consequences of the quasiclassical Langevin equation. This Langevin equation is an equation of motion of the classical type where, however, the stochastic Langevin force is correlated according to the quantum form of the dissipation-fluctuation theorem such that ultimately its power spectrum increases linearly with frequency. Most extensively, we have studied the decay of a metastable state driven by a stochastic force. For a particular type of potential well (piecewise parabolic), we have derived explicit expressions for the decay rate for an arbitrary power spectrum of the stochastic force. We have found that the quasiclassical Langevin equation leads to decay rates which are physically meaningful only within a very restricted range. We have also studied the influence of quantum fluctuations on a predominantly deterministic motion and we have found that there the predictions of the quasiclassical Langevin equations are correct.     

Probabilistic teleportation of an arbitrary GHZ-class state with a pure entangled two-particle quantum channel and its application in quantum state sharing

This paper presents a scheme for probabilistic teleportation of an arbitrary GHZ-class state with a pure entangled two-particle quantum channel. The sender Alice first teleports the coefficients of the unknown state to the receiver Bob, and then Bob reconstructs the state with an auxiliary particle and some unitary operations if the teleportation succeeds. This scheme has the advantage of transmitting much less particles for teleporting an arbitrary GHZ-class state than others. Moreover, it discusses the application of this scheme in quantum state sharing.     

Ramsey numbers and adiabatic quantum computing

The graph-theoretic Ramsey numbers are notoriously difficult to calculate. In fact, for the two-color Ramsey numbers R(m,n) with m, n≥3, only nine are currently known. We present a quantum algorithm for the computation of the Ramsey numbers R(m,n). We show how the computation of R(m,n) can be mapped to a combinatorial optimization problem whose solution can be found using adiabatic quantum evolution. We numerically simulate this adiabatic quantum algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(2,s) for 5≤s≤7. We then discuss the algorithm's experimental implementation, and close by showing that Ramsey number computation belongs to the quantum complexity class quantum Merlin Arthur.     

Nanomagnet coupled to quantum spin Hall edge: An adiabatic quantum motor

The precessing magnetization of a magnetic islands coupled to a quantum spin Hall edge pumps charge along the edge. Conversely, a bias voltage applied to the edge makes the magnetization precess. We point out that this device realizes an adiabatic quantum motor and discuss the efficiency of its operation based on a scattering matrix approach akin to Landauer–Büttiker theory. Scattering theory provides a microscopic derivation of the Landau–Lifshitz–Gilbert equation for the magnetization dynamics of the device, including spin-transfer torque, Gilbert damping, and Langevin torque. We find that the device can be viewed as a Thouless motor, attaining unit efficiency when the chemical potential of the edge states falls into the magnetization-induced gap. For more general parameters, we characterize the device by means of a figure of merit analogous to the ZT value in thermoelectrics.     

Nonadiabatic corrections to a quantum dot quantum computer working in adiabatic limit

The time of operation of an adiabatic quantum computer must be less than the decoherence time, otherwise the computer would be nonoperative. So far, the nonadiabatic corrections to an adiabatic quantum computer are merely theoretical considerations. By the above reason, we consider the particular case of a quantum-dot-confined electron spin qubit working adiabatically in the nanoscale regime (e.g., in the MeV range of energies) and include nonadiabatic corrections in it. If the decoherence times of a quantum dot computer are ～100 ns [J M Kikkawa and D D Awschalom, Phys. Rev. Lett. 80, 4313 (1998)] then the predicted number of one qubit gate (primitive) operations of the Loss–DiVincenzo quantum computer in such an interval of time must be >10 ¹⁰. However, if the quantum-dot-confined electron spin qubit is very excited (i.e., the semiclassical limit) the number of operations of such a computer would be approximately the same as that of a classical computer. Our results suggest that for an adiabatic quantum computer to operate successfully within the decoherence times, it is necessary to take into account nonadiabatic corrections.     

Trapping and cooling a mirror to its quantum mechanical ground state

We propose a technique aimed at cooling a harmonically oscillating mirror to its quantum mechanical ground state starting from room temperature. Our method, which involves the two-sided irradiation of the vibrating mirror inside an optical cavity, combines several advantages over the two-mirror arrangements being used currently. For comparable parameters the three-mirror configuration provides a stiffer trap for the oscillating mirror. Furthermore, it prevents bistability from limiting the use of higher laser powers for mirror trapping, and also partially does so for mirror cooling. Lastly, it improves the isolation of the mirror from classical noise so that the quantum mechanical dynamics of the mirror become easier to observe. These improvements are expected to bring the task of achieving and detecting ground state occupation for the mirror closer to completion.     

Universal and deterministic manipulation of the quantum state of harmonic oscillators: a route to unitary gates for Fock state qubits

We present a simple quantum circuit that allows for the universal and deterministic manipulation of the quantum state of confined harmonic oscillators. The scheme is based on the selective interactions of the referred oscillator with an auxiliary three-level system and a classical external driving source, and enables any unitary operations on Fock states, two by two. One circuit is equivalent to a single qubit unitary logical gate on Fock states qubits. Sequences of similar protocols allow for complete, deterministic, and state-independent manipulation of the harmonic oscillator quantum state.     

Crossover from adiabatic to antiadiabatic quantum pumping with dissipation

Quantum pumping, in its different forms, is attracting attention from different fields, from fundamental quantum mechanics, to nanotechnology, to superconductivity. We investigate the crossover of quantum pumping from the adiabatic to the antiadiabatic regime in the presence of dissipation, and find general and explicit analytical expressions for the pumped current in a minimal model describing a system with the topology of a ring forced by a periodic modulation of frequency ω. The solution allows following in a transparent way the evolution of pumped dc current from much smaller to much larger ω values than the other relevant energy scale, the energy splitting introduced by the modulation. We find and characterize a temperature-dependent optimal value of the frequency for which the pumped current is maximal.     

Acceleration of adiabatic quantum state transfer in a spin chain under zero-energy-change pulse control

We present a protocol for accelerating adiabatic quantum state transfer through a spin chain by adding an effective control pulse. Using Feshbach P-Q partitioning technique, we obtain the one-component dynamical equation which guides us to set the amplitude and period of the control field. This field can be a sequence of alternatively negative and positive (zero-energy change) pulses which can be realized easily in experiment. As an example, we discuss a three particles spin chain and the numerical calculation shows that the accelerated quantum state transfer can be obtained.     

含时磁共振系统的精确解和绝热近似解

在瞬时本征态完备基矢下,把一个经典含时磁共振系统的薛定谔方程转化为二阶常系数微分方程,实现了该量子系统的精确求解.利用该系统的精确解,讨论了绝热近似的精确程度,非常清晰地刻画了绝热近似解和精确解在量子态分布概率上的差异.结果表明,若系统初态制备于某个瞬时本征态上,系统保持在该瞬时本征态的概率介于0.888 9～1之间,...     

An application of Bell's inequalities to a quantum state extension problem

Using techniques from the study of quantum violations of Bell's inequalities, we give examples of three C ^*-algebras A, B, C, and states ₁₂ on A B, and ₂₃ on B C, which agree on B, but do not have a common extension to A B C. This situation cannot occur in classical probability, i.e. for commutative algebras.     

Adiabatic anholonomy and canonical transformations

Biswas and Soni [4] have surmised a semiclassical formula for Berry’s phase in terms of a generating function. We derive this formula apart from showing that it is not true in general and investigate its domain of validity. We also derive transformation formulae for Berry’s phase (Hannay’s angle) under general canonical transformations. A simpler proof for total angle invariance than hitherto available, is given.     

共轭线性对称性及其对PT-对称量子理论的应用

传统量子系统的哈密顿是自伴算子,哈密顿的自伴性不仅保证系统遵循酉演化和保持概率守恒,而且也保证了它自身具有实的能量本征值,这类系统称为自伴量子系统.然而,确实存在一些物理系统(如PT-对称量子系统),其哈密顿不是自伴的,这类系统称为非自伴量子系统.为了深入研究PT-对称量子系统,并考虑到算子PT的共轭线性性,首先讨论了共轭线性算子的一些性质,包括它们的矩阵表示和谱结构等;其次,分别研究了具有共轭线性对称性和完整共轭线性对称性的线性算子,通过它们的矩阵表示,给出了共轭线性对称性和完整共轭线性对称性的等价刻画;作为应用,得到了关于PT-对称及完整PT-对称算子的一些有趣性质,并通过一些具体例子,说明了完整PT-对称性对张量积运算不具有封闭性,同时说明了完整PT-对称性既不是哈密顿算子在某个正定内积下自伴的充分条件,也不是必要条件.     

Spatial interference of coherent atomic waves by manipulation of the internal quantum state

A trapped >(87)Rb Bose-Einstein condensate is initially put into a superposition of two internal states. Under the effect of gravity and by means of a second transition, we prepare two vertically displaced condensates in the same internal state. These constitute two coherent sources of matter waves with adjustable spatial separation. Fringe patterns, observed after free expansion, are associated with the interplay between internal and external degrees of freedom and substantially agree with those for a double-slit experiment.     

Four-mode coherent-entangled state and its application

A new kind of four-mode continuous variable coherent-entangled state is proposed in the Fock space by using the technique of integration within an ordered product, which exhibits both the properties of a coherent state and an entangled state, and spans a complete and orthonormal representation. The conjugate state of the four-mode continuous variable coherent-entangled state is derived by using the Fourier transformation. Moreover, a simple experimental protocol of generating a four-mode continuous variable coherent-entangled state is proposed by using beam splitters. As applications of this four-mode continuous variable coherent-entangled state, a four-mode entangled state and a four-mode squeezing-Fresnel operator are constructed.     

Four-mode coherent-entangled state and its application

A new kind of four-mode continuous variable coherent-entangled state is proposed in the Fock space by using the technique of integration within an ordered product,which exhibits both the properties of a coherent state and an entangled state,and spans a complete and orthonormal representation.The conjugate state of the four-mode continuous variable coherent-entangled state is derived by using the Fourier transformation.Moreover,a simple experimental protocol of generating a four-mode continuous variable coherent-entangled state is proposed by using beam splitters.As applications of this four-mode continuous variable coherent-entangled state,a four-mode entangled state and a four-mode squeezing-Fresnel operator are constructed.     

All-solid-state continuous-wave laser systems for ionization,cooling and quantum state manipulation of beryllium ions

We describe laser systems for photoionization, Doppler cooling, and quantum state manipulation of beryllium ions. For photoionization of neutral beryllium, we have developed a continuous-wave 235 nm source obtained by two stages of frequency doubling from a diode laser at 940 nm. The system delivers up to 400 mW at 470 nm and 28 mW at 235 nm. For control of the beryllium ion, three laser wavelengths at 313 nm are produced by sum-frequency generation and second-harmonic generation from four infrared fiber lasers. Up to 7.2 W at 626 nm and 1.9 W at 313 nm are obtained using two pump beams at 1051 and 1551 nm. Intensity drifts of around 0.5 % per hour have been measured over 8 h at a 313 nm power of 1 W. These systems have been used to load beryllium ions into a segmented ion trap.     

Shannon dimensionality of quantum channels and its application to photon entanglement

We introduce the concept of Shannon dimensionality D as a new way to quantify bipartite entanglement as measured in an experiment. This is applied to orbital-angular-momentum entanglement of two photons, using two state analyzers composed of a rotatable angular-sector phase plate that is lens coupled to a single-mode fiber. We can deduce the value of D directly from the observed two-photon coincidence fringe. In our experiment, D varies between 2 and 6, depending on the experimental conditions. We predict how the Shannon dimensionality evolves when the number of angular sectors imprinted in the phase plate is increased and anticipate that D approximately 50 is experimentally within reach.