Rabi oscillations and Ramsey-type pulses in ultracold bosons: Role of interactions

Abstract

Double-well systems loaded with one, two, or many quantum particles give rise to intriguing dynamics, ranging from Josephson oscillation to self-trapping. This work presents theoretical and experimental results for two distinct double-well systems, both created using dilute rubidium Bose-Einstein condensates with particular emphasis placed on the role of interaction in the systems. The first is realized by creating an effective two-level system through Raman coupling of hyperfine states. The second is an effective two-level system in momentum space generated through the coupling by an optical lattice. Even though the non-interacting systems can, for a wide parameter range, be described by the same model Hamiltonian, the dynamics for these two realizations differ in the presence of interactions. The difference is attributed to scattering diagrams that contribute in the lattice coupled system but vanish in the Raman coupled system. The internal dynamics of the Bose-Einstein condensates for both coupling scenarios is probed through a Ramsey-type interference pulse sequence, which constitutes a key building block of atom interferometers. These results have important implications in a variety of contexts including lattice calibration experiments and momentum space lattices used for quantum analog simulations.

Effect of interactions in the interference pattern of Bose-Einstein condensates

“…In Sec. III we present a theoretical analysis of the simplest scenario of two interfering condensates [1,34], revealing that the phase modification due to mutual interactions is not fully captured by an effective force arising from the repulsion between the two wave packets, as considered for example in [2,25,31]. In particular, we evidence a local modification of the phase in the region where the two condensates superimpose.…”

“…Then, in order to account for the effect of the mutual repulsion, we consider an approach that has been often used in the literature, namely we assume that the phase of the two condensates is modified by an additional velocity term produced by an effective force due to the mean-field interaction of the two condensates [2,25,31]. According to the discussion in [31] [see their Eq. 34], the effective force (that here acts along one of the strongly confined directions of the trap) can be written as…”

“…Though not explicitly mentioned in Ref. [31], in the derivation of Eq. 3there is the implicit assumption that the two condensates substantially overlap.…”

“…Despite repeated scrutiny [23][24][25][26], in the presence of interactions even the basic phenomenon of two interfering condensates still shows interesting and unraveled features [27][28][29]. At the mean-field level, the self-interaction of an individual condensate drives its phase evolution [30], while the mutual interactions between two condensates are usually taken into account via the modification of the condensates center-of-mass motion [2,25,31]. In doing so, the implicit assumption is made that the condensate phase is "rigid" [32,33], i.e., not locally deformable but only globally variable.…”

“…The integrated density distribution of the interferogram is analyzed performing a Fourier transform (FT). The main wave vector obtained from the Fourier analysis is compared with (i) the analytical expression for two expanding condensates neglecting their mutual interaction, (ii) the prediction including mutual interaction through an effective force [31], and (iii) with numerical GP simulations. The measurements clearly show that the mutual interaction between the two expanding condensates modifies their phase evolution.…”