A synthetic electric force acting on neutral atoms

Abstract

Electromagnetism is a simple example of a gauge theory where the underlying potentials (the vector and scalar potentials) are defined only up to a gauge choice. The vector potential generates magnetic fields through its spatial variation and electric fields through its time dependence 1 . Here, we report experiments in which we have produced a synthetic gauge field. The gauge field emerges only at low energy in a rubidium BoseEinstein condensate: the neutral atoms behave as charged particles do in the presence of a homogeneous effective vector potential 2 . We have generated a synthetic electric field through the time dependence of an effective vector potential, a physical consequence that emerges even though the vector potential is spatially uniform.Gauge theories play a central role in modern quantum physics. In some cases, they can be viewed as emerging as the low-energy description of a more complete theory 3,4 . Electromagnetism is the best known gauge theory and its gauge fields are the ordinary scalar and vector potentials. Magnetic fields arise only from spatial variations of the vector potential, whereas electric fields arise from both time variations of the vector potential and gradients of the scalar potential. These potentials are defined only to within a gauge choice, where for a charged particle the canonical momentum (the variable canonically conjugate to position) and the mechanical momentum (the mass times the velocity) are not equal. Our experiments 2 have realized a particular version 5 of a class of proposals 6-11 to generate effective vector potentials for neutral atoms through interactions with laser light, and have created synthetic magnetic fields 12 important for simulating charged condensed-matter systems with neutral atoms 13,14 . Here we demonstrate the complementary phenomenon: a synthetic electric field generated from a time-dependent effective vector potential. Additionally, we make independent measurements of both the mechanical momentum and canonical momentum, where the latter is usually not possible.The electromagnetic vector potential A for a charged particle appears in the Hamiltonian H = (p can − qA) 2 /2m, where p can is the canonical momentum, q is the charge and m is the mass. (p can −qA = mv is the mechanical momentum for a particle moving with velocity v.) We recently demonstrated a technique to engineer Hamiltonians of this form for ultracold atoms, and prepared a Bose-Einstein condensate (BEC) at rest with an effective vector potential A = A xx constant in time and space 2 , corresponding to E = B = 0, where E and B are the synthetic electric field and synthetic magnetic field for neutral atoms, respectively. In ref. 12, we made A depend on position, giving B = ∇ × A = 0 but E = 0. Here we add time dependence to a spatially uniform vector potential A(t ) = A(t )x, generating a synthetic electric field E(t )x = −∂A/∂t . The resulting force is distinct from that arising from gradients of scalar potentials φ(r), for example, from an external trapping potential. A revealin...

Thermodynamic properties of rotating trapped ideal Bose gases

“…In this case, atoms behave like charged particles in magnetic field. The "synthetic" magnetic field has already been realized in experiments and can be produced significantly large, which makes it hopefully to achieve the fast-rotating limit [14][15][16].…”

“…More recently, the so-called "synthetic" magnetic field approach is developed [14][15][16], which creates an effective gauge potential A for neutral atoms by means of optical field [17][18][19], instead of rotating the frame. In this case, atoms behave like charged particles in magnetic field.…”

Valley-dependent gauge fields for ultracold atoms in square optical superlattices

“…Interestingly, a time-dependent but valleyindependent vector potential associated with an effective electric field for neutral atoms was created by tuning the detuning in the laser-atom coupling with time [29]. In contrast, we have proposed a feasible scheme to realize the tunable valley-dependent gauge fields (including electric field) in a square optical superlattice.…”

Moving obstacle potential in a spin-orbit-coupled Bose-Einstein condensate

“…The successful experimental realization of various synthetic gauge fields and spin-orbit coupling (SOC) in BoseEinstein condensates (BECs) has recently drawn considerable theoretical attention [1][2][3][4][5][6][7][8][9][10], with a number of studies addressing the ground state structures and static properties of topological excitations (for recent reviews, see, for example, Refs. [11][12][13]).…”