arXiv subjects

Kelin Gao

Publications and source records attributed to Kelin Gao.

35 records · Page 2Linked to original sources

arXiv2003

Quasi-spin Model for Macroscopic Quantum Tunnelling between Two Coupled Bose-Einstein Condensates

The macroscopic quantum tunneling between two coupled Bose-Einstein condensates (BEC) (radio-frequency coupled two-component BECs or two BECs confined in a double-well potential) is mapped onto the tunneling of an uniaxial spin with an applied magnetic field. The tunneling exponent is calculated with an imaginary-time path-integral method. In the limit of low barrier, the dependence of tunneling exponent on the system parameters is obtained, and the crossover temperature from thermal regime to quantum regime is estimated. The detailed information about the tunnelling will give help to control population conversion between coupled BECs and realize quantum computation with coupled BECs.

cond-mat.mes-hall↗

arXiv2003

Phase-Dependent Spontaneous Spin Polarization and Bifurcation Delay in Coupled Two-Component Bose-Einstein Condensates

The spontaneous spin polarization and bifurcation delay in two-component Bose-Einstein condensates coupled with laser or/and radio-frequency pulses are investigated. We find that the bifurcation and the spontaneous spin polarization are determined by both physical parameters and relative phase between two condensates. Through bifurcations, the system enters into the spontaneous spin polarization regime from the Rabi regime. We also find that bifurcation delay appears when the parameter is swept through a static bifurcation point. This bifurcation delay is responsible for metastability leading to hysteresis.

cond-mat.mes-hall↗

arXiv2003

Implementation for Solving Random Satisfiability Problems through CNOT-based circuits in a NMR Quantum Processor

We give a general method of construting quantum circuit for random \QTR{it}{satisfiability} (SAT) problems with the basic logic gates such as multi-qubit controlled-NOT and NOT gates. The sizes of these circuits are almost the same as the sizes of the SAT formulas. Further, a parallelization scheme is described to solve random SAT problems efficiently through these quantum circuits in \QTR{it}{nuclear magnetic resonance} (NMR) ensemble quantum computing. This scheme exploits truly mixed states as input states rather than pseudo-pure states, and combines with the topological nanture of the NMR spectrum to identify the solutions to SAT problems in a parallel way. Several typical SAT problems have been experimentally demonstrated by this scheme with good performances.

quant-ph↗

arXiv2003

Experimental demonstration of the interferometric complementarity of one- and two-particle interference in a bulk Nuclear Magnetic Resonance ensemble

We analyze an interferometric complementarity between one- and two-particle interference in the general case: $V_{i}^{2}+V_{12}^{2}\leq 1$ $(i=1$, $2)$, and further examine the relation among one-particle interference visibility $V_{i}$, two-particle interference visibility $V_{12}$ and the predication $P_{i}$ of the path of a single particle. An equality $V_{i}^{2}+V_{12}^{2}+P_{i}^{2}=1$ $(i=1$, $2)$ is achieved for any pure two-particle source, which implies the condition of the complementarity relation to reach the upper bound and its relation to another interferometric complementarity between path information and interference visibility of a single particle. Meanwhile, the relationships of the complementarities and the entanglement $E$ of the composite system are also investigated. Using nuclear magnetic resonance techniques, the two-particle interferometric complementarity was experimentally tested with the ensemble-averaged spin states, including two extreme cases and an intermediate case.

quant-ph↗

arXiv2003

Wave-packet trains of a time-dependent harmonic oscillator

By using a test-function method, we construct $n$ exact solutions of a quantum harmonic oscillator with a time-dependent "spring constant". Any $n$-th solution describes a wave-packet train consisting of $n+1$ packets. Its center oscillates like the classically harmonic oscillator with variable frequency, and width and highness of each packet change simultaneously. When the deformation is small, it behaves like a soliton train, and the large deformation is identified with collapse and revival of the wave-packet train.

quant-ph↗

arXiv2003

An interferometric complementarity experiment in a bulk Nuclear Magnetic Resonance ensemble

We have experimentally demonstrated the interferometric complementarity, which relates the distinguishability $D$ quantifying the amount of which-way (WW) information to the fringe visibility $V$ characterizing the wave feature of a quantum entity, in a bulk ensemble by Nuclear Magnetic Resonance (NMR) techniques. We primarily concern on the intermediate cases: partial fringe visibility and incomplete WW information. We propose a quantitative measure of $D$ by an alternative geometric strategy and investigate the relation between $D$ and entanglement. By measuring $D$ and $V$ independently, it turns out that the duality relation $D^{2}+V^{2}=1$ holds for pure quantum states of the markers.

quant-ph↗

arXiv2002

Conditional Spontaneous Spin Polarization and Bifurcation Delay in Coupled Two-Component Bose-Einstein Condensates

The spontaneous spin polarization and bifurcation delay in two-component Bose-Einstein condensates coupled with Raman pulses are investigated. We find that the bifurcation and the spontaneous spin polarization depend not only on the system parameters, but also on the relative phase between two components. Through bifurcations, the system enters into the spontaneous spin polarization regime from the Rabi regime. We also find that bifurcation delay appears when the parameter is swept through the static bifurcation point. This bifurcation delay is responsible for metastability leading to hysteresis. The area enclosed in the hysteresis loop increases with the sweeping rate of the parameter.

cond-mat.mes-hall↗

arXiv2002

Nuclear Magnetic Resonance Implemenations of Remote State Preparation of Arbitary Longitudinal Qubit and Remote State Measurement of a Qubit

A qubit chosen from equatorial or polar great circles on a Bloch sphere can be remotely prepared with an Einstain-Podolsky-Rosen (EPR) state shared and a cbit communication. We generalize this protocal into an arbitrary longitudinal qubit on the Bloch sphere in which the azimuthal angle phi can be an arbitrary value instead of only being zero. The generalized scheme was experimentally realized using liquid-state nuclear magnetic resonance (NMR) techniques. Also, we have experimentally demonstrated remote state measurement (RSM) on an arbitary qubit proposed by Pati.

quant-ph↗

arXiv2002

Exhibition of the periodicity of Quantum Fourier Transformation in Nuclear Magnetic Resonance

The remarkable capability of quantum Fourier transformation (QFT) to extract the periodicity of a given periodic function has been exhibited by using nuclear magnetic resonance (NMR) techniques. Two separate sets of experiments were performed. In a full QFT, the periodicity were validated with state tomography and fidelity measurements. For a simplified QFT, the three-qubit pseudo-pure state was created by introducting an additional observer spin, and the spectra recorded on the observer spin showed intuitively the power of QFT\ to find the periodicity. Experimentally realizing the QFT provides a critical step to implement the renowned Shor's quantum factoring algorithm and many other algorithms. Moveover, it can be applied to the study of quantum chaos and other quantum information processing.

quant-ph↗

arXiv2002

Experimental Implementation of Remote State Preparation by Nuclear Magnetic Resonance

We have experimentally implemented remote state preparation (RSP) of a qubit from a hydrogen to a carbon nucleus in molecules of carbon-13 labeled chloroform $^{13}$CHCl$_{3}$ over interatomic distances using liquid-state nuclear magnetic resonance (NMR) technique. Full RSP of a special ensemble of qubits, i.e., a qubit chosen from equatorial and polar great circles on a Bloch sphere with Pati's scheme, was achieved with one cbit communication. Such a RSP scheme can be generalized to prepare a large number of qubit states and may be used in other quantum information processing and quantum computing.

quant-ph↗

arXiv2001

Avalanche dynamics in Bak-Sneppen evolution model observed with standard distribution width of fitness

We introduce the standard distribution width of fitness to characterize the global and individual features of a ecosystem in the Bak-Sneppen evolution model. Through tracking this quantity in evolution, a different hierarchy of avalanche dynamics, $w_{0}$ avalanche is observed. The corresponding gap equation and the self-organized threshold $w_{c}$ are obtained. The critical exponents $τ,$ $γ$and $ρ$, which describe the behavior of the avalanche size distribution, the average avalanche size and the relaxation to attractor, respectively, are calculated with numerical simulation. The exact master equation and $γ$ equation are derived. And the scaling relations are established among the critical exponents of this new avalanche.

nlin.AO↗

arXiv2001

Quantum Computation Based on Magic-Angle-Spinning Solid State Nuclear Magnetic Resonance Spectroscopy

Magic-angle spinning (MAS) solid state nuclear magnetic resonance (NMR) spectroscopy is shown to be a promising technique for implementing quantum computing. The theory underlying the principles of quantum computing with nuclear spin systems undergoing MAS is formulated in the framework of formalized quantum Floquet theory. The procedures for realizing state labeling, state transformation and coherence selection in Floquet space are given. It suggests that by this method, the largest number of qubits can easily surpass that achievable with other techniques. Unlike other modalities proposed for quantum computing, this method enables one to adjust the dimension of the working state space, meaning the number of qubits can be readily varied. The universality of quantum computing in Floquet space with solid state NMR is discussed and a demonstrative experimental implementation of Grover's search is given.

quant-ph↗

arXiv2001

Experimental Implementation of Hogg's Algorithm on a Three-Quantum-bit NMR Quantum Computer

Using nuclear magnetic resonance (NMR) techniques with three-qubit sample, we have experimentally implemented the highly structured algorithm for the 1-SAT problem proposed by Hogg. A simplified temporal averaging procedure was employed to the three-qubit spin pseudo-pure state. The algorithm was completed with only a single evaluation of structure of the problem and the solutions were found with probability 100%, which outperform both unstructured quantum and the best classical search algorithm.

quant-ph↗

arXiv2001

Classical calculation of high-order harmonic generation of atomic and molecular gases in intense laser fields

Based upon our previous works (Eur.Phys.J.D 6, 319(1999); Chin.Phys.Lett. 18, 236(2001)), we develop a classical approach to calculate the high-order harmonic generation of the laser driven atoms and molecules. The Coulomb singularities in the system have been removed by a regularization procedure. Action-angle variables have been used to generate the initial microcanonical distribution which satisfies the inversion symmetry of the system. The numerical simulation show, within a proper laser intensity, a harmonic plateau with only odd harmonics appears. At higher intensities, the spectra become noisier because of the existence of chaos. With further increase in laser intensity, ionization takes place, and the high-order harmonics disappear. Thus chaos introduces noise in the spectra, and ionization suppresses the harmonic generation, with the onset of the ionization follows the onset of chaos.

physics.atom-ph↗

arXiv2000

Chaotic atomic population oscillations between two coupled Bose-Einstein condensates with time-dependent asymmetric trap potential

We have investigated the chaotic atomic population oscillations between two coupled Bose-Einstein condensates (BEC) with time-dependent asymmetric trap potential. In the perturbative regime, the population oscillations can be described by the Duffing equation, and the chaotic oscillations near the separatrix solution are analyzed. The sufficient-necessary conditions for stable oscillations depend on the physical parameters and initial conditions sensitively. The first-order necessary condition indicates that the Melnikov function is equal to zero, so the stable oscillations are Melnikov chaotic. For the ordinary parameters and initial conditions, the chaotic dynamics is simulated with numerical calculation. If the damping is absent, with the increasing of the trap asymmetry, the regular oscillations become chaotic gradually, the corresponding stroboscopic Poincare sections (SPS) vary from a single island to more islands, and then the chaotic sea. For the completely chaotic oscillations, the long-term localization disappears and the short-term localization can be changed from one of the BECs to the other through the route of Rabi oscillation. When there exists damping, the stationary chaos disappears, the transient chaos is a common phenomenon before regular stable frequency locked oscillations. And proper damping can keep localization long-lived.

quant-ph↗

arXiv2000

Experimental Test of Complementarity by Nuclear Magnetic Resonance Techniques

We have tested complementarity for the ensemble-averaged spin states of nuclei $^{13}$C in the molecule of $^{13}$CHCl$_{3}$ by the use of the spin states of another nuclei $^{1}$H as the path marker. It turns out that the wave-particle duality holds when one merely measures the probability density of quantum states, and that the wave- and particle-like behavior is simultaneously observed with the help of measuring populations and coherence in a single nuclear magnetic resonance(NMR) experiment. Effects of path-marking schemes and causes of the appearance and disappearance of the wave behavior are analysed.

quant-ph↗

arXiv2000

Experimental realization of a highly structured search algorithm

The highly structured search algorithm proposed by Hogg[Phys.Rev.Lett. 80,2473(1998)] is implemented experimentally for the 1-SAT problem in a single search step by using nuclear magnetic resonance technique with two-qubit sample. It is the first demonstration of the Hogg's algorithm, and can be readily extended to solving 1-SAT problem for more qubits in one step if the appropriate samples possessing more qubits are experimentally feasible.

quant-ph↗