Spinor Bose-Einstein condensate interferometer within the undepleted pump approximation: Role of the initial state

Abstract

Most interferometers operate with photons or dilute, non-condensed cold atom clouds in which collisions are strongly suppressed. Spinor Bose-Einstein condensates (BECs) provide an alternative route toward realizing three-mode interferometers; in this realization, spin-changing collisions provide a resource that generates mode entanglement. Working in the regime where the pump mode, i.e., the m = 0 hyperfine state, has a much larger population than the side or probe modes (m = ±1 hyperfine states), f = 1 spinor BECs approximate SU(1,1) interferometers. We derive analytical expressions within the undepleted pump approximation for the phase sensitivity of such an SU(1,1) interferometer for two classes of initial states: pure Fock states and coherent spin states. The interferometer performance is analyzed for initial states without seeding, with single-sided seeding, and with double-sided seeding. The validity regime of the undepleted pump approximation is assessed by performing quantum calculations for the full spin Hamiltonian. Our analytical results and the associated dynamics are expected to guide experiments as well as numerical studies that explore regimes where the undepleted pump approximation makes quantitatively or qualitatively incorrect predictions.

Tailored generation of quantum states in an entangled spinor interferometer to overcome detection noise

“…Typical experiments studying pair production dynamics in a spinor BEC focus on initial conditions where the majority of the condensate populates the m F = 0 state and acts as a source for correlated pairs in m F = ±1. Here, we consider initial states where a BEC of N atoms is prepared in the m F = 0 mode, before a small number of atoms, n s , are coherently transferred to either of the m F = ±1 modes by, e.g., resonant microwaves [19], to act as a coherent seed that stimulates the spin-changing collisions [35,36,45].…”

“…Here, we have assumed the m F = 0, 1 modes are described as coherent states with occupation n1 (0) = ψ 0 |n 1 |ψ 0 = n s and n0 (0) = N − n s [35], respectively, while the m F = −1 mode is prepared in the vacuum state with n−1 = 0. Without loss of generality we have taken the m F = 0 coherent state to have a real amplitude, such that any relevant phase relationship between the m F = 0, ±1 modes is encoded in θ s .…”

“…[46]). This initial condition offers a wide range of tunability in terms of, e.g., relative particle number and phase between the m F = ±1 modes [35], but we will choose to focus on the specific initial configuration described by,…”

“…We assume a condensate of N = 10 4 atoms is prepared in the m F = 0 mode before a small number of atoms is coherently transferred to seed the m F = 1 mode. We model this transfer process formally such that the total number of atoms N is fixed in our calculations and we do not truncate our Fock basis [35]. For this large particle number our initial state very well approximates…”

“…In this context, this manuscript presents a systematic investigation of the robustness and realistic metrological potential of a class of atomic entangled states for SU(2) atom interferometry with spinor BECs. Our study is targeted towards applications where entangled matter waves are spatially split and recombined to measure, e.g., gravitational acceleration, and are thus ill-suited to the widely studied IBR methods that underpin related SU (1,1) atom interferometry [22,[35][36][37]. We investigate the use of spin-changing collisions in a spinor BEC to generate atomic squeezing and entanglement, and show that entangled states generated by triggering the collisions with a small classical seed rather than vacuum fluctuations are more robust to realistic detection noise when using simple measurement observables.…”