A theoretical model of computation is proposed based on Lorentz quantum mechanics.Besides the standard qubits,this model has an additional bit,which we call hyperbolic bit(or hybit in short).A set of basic logical gat...A theoretical model of computation is proposed based on Lorentz quantum mechanics.Besides the standard qubits,this model has an additional bit,which we call hyperbolic bit(or hybit in short).A set of basic logical gates are constructed and their universality is proved.As an application,a search algorithm is designed for this computer model and is found to be exponentially faster than Grover's search algorithm.展开更多
We propose a general variational principle for mapping the interacting systems in continuous space to lattice models.Based on the principle,we derive a set of self-consistent nonlinear equations for the Wannier functi...We propose a general variational principle for mapping the interacting systems in continuous space to lattice models.Based on the principle,we derive a set of self-consistent nonlinear equations for the Wannier functions(or,equivalently for the Bloch functions).These equations show that the Wannier functions can be strongly influenced by the interaction and be significantly different from their non-interacting counterparts.The approach is demonstrated with interacting bosons in an optical lattice,and illustrated quantitatively by a simple model of interacting bosons in a double well potential.It is shown that the so-determined lattice model parameters can be significantly different from their non-interacting values.展开更多
Liquid helium 4 had been the only bosonic superfluid available in experiments for a long time. This situation was changed in 1995, when a new superfluid was born with the realization of the Bose-Einstein condensation ...Liquid helium 4 had been the only bosonic superfluid available in experiments for a long time. This situation was changed in 1995, when a new superfluid was born with the realization of the Bose-Einstein condensation in ultracold atomic gases. The liquid helium 4 is strongly interacting and has no spin; there is almost no way to change its parameters, such as interaction strength and density. The new superfluid, Bose-Einstein condensate （BEC）, offers various advantages over liquid helium. On the one hand, BEC is weakly interacting and has spin degrees of freedom. On the other hand, it is convenient to tune almost all the parameters of a BEC, for example, the kinetic energy by spin--orbit coupling, the density by the external potential, and the interaction by Feshbach resonance. Great efforts have been devoted to studying these new aspects, and the results have greatly enriched our understanding of superfluidity. Here we review these developments by focusing on the stability and critical velocity of various superfluids. The BEC systems considered include a uniform superfluid in free space, a superfluid with its density periodically modulated, a superfluid with artificially engineered spinorbit coupling, and a superfluid of pure spin current. Due to the weak interaction, these BEC systems can be well described by the mean-field Gross-Pitaevskii theory and their superfluidity, in particular critical velocities, can be examined with the aid of Bogoliubov excitations. Experimental proposals to observe these new aspects of superfluidity are discussed.展开更多
We investigate a time-independent many-boson system,whose ground states are quasi-degenerate and become infinitely degenerate in the thermodynamic limit.Out of these quasi-degenerate ground states we construct a quant...We investigate a time-independent many-boson system,whose ground states are quasi-degenerate and become infinitely degenerate in the thermodynamic limit.Out of these quasi-degenerate ground states we construct a quantum state that evolves in time with a period that is logarithmically proportional to the number of particles,that is,T~log N.This boson system in such a state is a quantum time crystal as it approaches the ground state in the thermodynamic limit.The logarithmic dependence of its period on the total particle number N makes it observable experimentally even for systems with very large number of particles.Possible experimental proposals are discussed.展开更多
基金supported by the National Key R&D Program of China(Grant Nos.2017YFA0303302 and 2018YFA0305602)the National Natural Science Foundation of China(Grant No.11921005)Shanghai Municipal Science and Technology Major Project(Grant No.2019SHZDZX01)。
文摘A theoretical model of computation is proposed based on Lorentz quantum mechanics.Besides the standard qubits,this model has an additional bit,which we call hyperbolic bit(or hybit in short).A set of basic logical gates are constructed and their universality is proved.As an application,a search algorithm is designed for this computer model and is found to be exponentially faster than Grover's search algorithm.
基金Supported by the National Natural Science Foundation of China under Grant No 10825417.
文摘We propose a general variational principle for mapping the interacting systems in continuous space to lattice models.Based on the principle,we derive a set of self-consistent nonlinear equations for the Wannier functions(or,equivalently for the Bloch functions).These equations show that the Wannier functions can be strongly influenced by the interaction and be significantly different from their non-interacting counterparts.The approach is demonstrated with interacting bosons in an optical lattice,and illustrated quantitatively by a simple model of interacting bosons in a double well potential.It is shown that the so-determined lattice model parameters can be significantly different from their non-interacting values.
基金supported by the National Basic Research Program of China(Grant Nos.2013CB921903 and 2012CB921300)the National Natural Science Foundation of China(Grant Nos.11274024,11334001,and 11429402)
文摘Liquid helium 4 had been the only bosonic superfluid available in experiments for a long time. This situation was changed in 1995, when a new superfluid was born with the realization of the Bose-Einstein condensation in ultracold atomic gases. The liquid helium 4 is strongly interacting and has no spin; there is almost no way to change its parameters, such as interaction strength and density. The new superfluid, Bose-Einstein condensate （BEC）, offers various advantages over liquid helium. On the one hand, BEC is weakly interacting and has spin degrees of freedom. On the other hand, it is convenient to tune almost all the parameters of a BEC, for example, the kinetic energy by spin--orbit coupling, the density by the external potential, and the interaction by Feshbach resonance. Great efforts have been devoted to studying these new aspects, and the results have greatly enriched our understanding of superfluidity. Here we review these developments by focusing on the stability and critical velocity of various superfluids. The BEC systems considered include a uniform superfluid in free space, a superfluid with its density periodically modulated, a superfluid with artificially engineered spinorbit coupling, and a superfluid of pure spin current. Due to the weak interaction, these BEC systems can be well described by the mean-field Gross-Pitaevskii theory and their superfluidity, in particular critical velocities, can be examined with the aid of Bogoliubov excitations. Experimental proposals to observe these new aspects of superfluidity are discussed.
基金supported by the National Key R&D Program of China(Grant Nos.2017YFA0303302 and 2018YFA0305602)the National Natural Science Foundation of China(Grant No.11921005)Shanghai Municipal Science and Technology Major Project(Grant No.2019SHZDZX01)。
文摘We investigate a time-independent many-boson system,whose ground states are quasi-degenerate and become infinitely degenerate in the thermodynamic limit.Out of these quasi-degenerate ground states we construct a quantum state that evolves in time with a period that is logarithmically proportional to the number of particles,that is,T~log N.This boson system in such a state is a quantum time crystal as it approaches the ground state in the thermodynamic limit.The logarithmic dependence of its period on the total particle number N makes it observable experimentally even for systems with very large number of particles.Possible experimental proposals are discussed.
