Solving the Bose-Hubbard model with machine learning

Motivated by the recent successful application of artificial neural networks to quantum many-body problems [G. Carleo and M. Troyer, Science {\bf 355}, 602 (2017)], a method to calculate the ground state of the Bose-Hubbard model using a feedforward neural network is proposed. The results are in good agreement with those obtained by exact diagonalization and the Gutzwiller approximation. The method of neural-network quantum states is promising for solving quantum many-body problems of ultracold atoms in optical lattices.Comment: 4 pages, 4 figure

Many-body dynamics of a Bose--Einstein condensate collapsing by quantum tunneling

The dynamics of a Bose-Einstein condensate of atoms having attractive interactions is studied using quantum many-body simulations. The collapse of the condensate by quantum tunneling is numerically demonstrated and the tunneling rate is calculated. The correlation properties of the quantum many-body state are investigated.Comment: 6 pages, 3 figure

Can we swim in superfluids?: Numerical demonstration of self-propulsion in a Bose-Einstein condensate

It is numerically investigated whether a deformable object can propel itself in a superfluid. Articulated bodies and multi-component condensates are examined as swimmers. An articulated two-body swimmer cannot obtain locomotion without emitting excitations. More flexible swimmers can do so without the need to excite waves.Comment: 6 pages, 5 figures, 4 movies, jpsj class file correcte

Path-integral Monte Carlo study on a droplet of a dipolar Bose-Einstein condensate stabilized by quantum fluctuation

Motivated by the recent experiments [H. Kadau et al., Nature (London) 530, 194 (2016); I. Ferrier-Barbut et al., arXiv:1601.03318] and theoretical prediction (F. W\"achtler and L. Santos, arXiv:1601.04501), the ground state of a dysprosium Bose-Einstein condensate with strong dipole-dipole interaction is studied using the path-integral Monte Carlo method. It is shown that quantum fluctuation can stabilize the condensate against dipolar collapse.Comment: 4 pages, 3 figure

Dynamics of a vortex dipole across a magnetic phase boundary in a spinor Bose-Einstein condensate

Dynamics of a vortex dipole in a spin-1 Bose-Einstein condensate in which magnetic phases are spatially distributed is investigated. When a vortex dipole travels from the ferromagnetic phase to the polar phase, or vice versa, it penetrates the phase boundary and transforms into one of the various spin vortex dipoles, such as a leapfrogging ferromagnetic-core vortex dipole and a half-quantum vortex dipole. Topological connections of spin wave functions across the phase boundary are discussed.Comment: 8 pages, 6 figures, 7 movie

Self-rotation and synchronization in exciton-polariton condensates

Self-rotation occurs in an exciton-polariton condensate in a two-dimensional semiconductor microcavity pumped by a nonresonant Gaussian laser beam. A wave packet of the condensate spontaneously rotates around the center of the pumped region at a constant frequency breaking the rotation symmetry of the system. When two self-rotating condensates are created with an appropriate distance, synchronization occurs between the dynamics of the self-rotating condensates.Comment: 6 pages, 5 figures, 3 movie

Collision dynamics of Skyrmions in a two-component Bose-Einstein condensate

The dynamics of Skyrmions in a two-component Bose-Einstein condensate are numerically investigated in the mean-field theory. When two Skyrmions collide with each other, they are first united and then scattered into various states. For head-on collisions, Skyrmions with unit winding number are scattered. The collision dynamics with an impact parameter are shown to depend on the relative phase. These dynamic processes are characterized by integer winding numbers.Comment: 6 pages, 5 figures, 7 movie

Machine learning technique to find quantum many-body ground states of bosons on a lattice

We develop a variational method to obtain many-body ground states of the Bose-Hubbard model using feedforward artificial neural networks. A fully-connected network with a single hidden layer works better than a fully-connected network with multiple hidden layers, and a multi-layer convolutional network is more efficient than a fully-connected network. AdaGrad and Adam are optimization methods that work well. Moreover, we show that many-body ground states with different numbers of atoms can be generated by a single network.Comment: 8 pages, 10 figure

Quantum-Controlled Few-Photon State Generated by Squeezed Atoms

General principles and experimental schemes for generating a desired few-photon state from an aggregate of squeezed atoms are presented. Quantum-statistical information of the collective atomic dipole is found to be faithfully transferred to the photon state even in a few-photon regime. The controllability of few-photon states is shown to increase with increasing the number of squeezed atoms.Comment: 5 pages, RevTex, uses eclepsf.sty. The change is only one sentence referring to Ref.[4,7]. Accepted for publication in Physical Review Letter

Upper bound of one-magnon excitation and lower bound of effective mass for ferromagnetic spinor Bose and Fermi gases

Using a variational method, we derive an exact upper bound for one-magnon excitation energy in ferromagnetic spinor gases, which limits the quantum corrections to the effective mass of a magnon to be positive. We also derive an upper bound for one-magnon excitation energy in lattice systems. The results hold for both Bose and Fermi systems in $d$ dimensions as long as the interaction is local and invariant under spin rotation.Comment: 7 page