Measurement-Induced Dynamics of Particles and Quasiparticles in a Bose-Einstein-condensate array

TL;DR

The study analyzes how the bandwidth of a phase-contrast measurement on cold-atom systems governs what is observed and how the measurement backaction excites quasiparticles. By combining a two-level double-well toy model with a mean-field Bose-Hubbard/Bogoliubov treatment of a condensate, the authors derive two regimes: (i) wide-bandwidth measurements that effectively monitor bare particle occupancy and impart a Stark-like shift, and (ii) narrow-bandwidth measurements that, via a Schrieffer-Wolff transformation, couple to Bogoliubov quasiparticles and enable selective, mode-resolved probing. They show that wide-band measurements induce significant quasiparticle heating across the condensate, whereas narrow-band measurements can selectively suppress heating in a chosen quasiparticle mode by tuning the detuning $\

Abstract

Measurement plays a crucial role in a quantum system beyond just learning about the system state: it changes the post-measurement state and hence influences the subsequent time evolution; further, measurement can even create entanglement in the post-measurement conditional state. In this work, we study how careful choice of parameters for a typical measurement process on cold atoms systems -- phase contrast imaging -- has a strong impact on both what the experimentalist observes but also on the backaction the measurement has on the system, including the creation and diffusion of quasiparticles emerging from the quantum many-body dynamics. We focus on the case of a Bose-Einstein-condensate array, in the low-temperature and low-momentum limit. Our theoretical investigation reveals regimes where the imaging light probes either the bare particle or quasiparticle dynamics. Moreover, we find a path to selectively measuring quasiparticle modes directly, as well as controlling over the measurement-induced creation and diffusion of quasiparticles into different momentum states. This lays a foundation for understanding the effects of both experimental approaches for probing many-body systems, but also more speculative directions such as observable consequences of `spontaneous collapse' predictions from novel models of quantum gravity on aspects of the Standard Model.

Figures (13)

• Figure 1: (a) Schematic of a weakly probed atom in a double-well potential. (b) The effective tunneling atom in the wide-bandwidth regime. Adiabatic elimination of the fast probe state only introduces a Stark-like detuning in $\ket{L}$ (or equivalently a Stark-like shift to $\delta_R$ of $\ket{R}$, as explained below), while retaining the tunneling rate $t$ between the double-well states. Notice that the effective shelving jump operator measures the probability of the atom being in the state $\ket{L}$. (c) The effective tunneling atom in the narrow bandwidth. Adiabatic elimination of the now dynamical probe state introduces both a detuning at $\ket{L}$ and a shift to the tunneling rate $t$, as a result of perturbatively absorbing and eliminating the probe state interaction. Notice that the jump operator is a superposition of shelving at $\ket{L}$ and driving a transition from $\ket{R}$ top $\ket{L}$, which means measuring a superposition of $\ket{R}$ and $\ket{L}$.
• Figure 2: A diagram describing the measurement bandwidths of interest ($\kappa$ fixed). In the wide bandwidth regime, the tunneling atom does not "see" the drive between $\ket{L}$ and $\ket{r}$ due to the large detuning $\Delta$ and damping rate $\kappa$, but the drive strength $\Omega$ is still comparable to the energetic parameters of the atom. In the narrow bandwidth regime, the detuning and damping are not necessarily large, but the drive strength $\Omega$ is small enough to act perturbatively on the atom.
• Figure 4: The correspondence between bare bosons (in momentum space) and Bogoliubov quasiparticles, described by the relative ratio between Bogoliubov parameters as function of momentum norm. In higher momenta (or higher excitations), the bosons behave more like a quasiparticle.
• Figure 6: Quasiparticle heating over time for $N=7$ due to loss.
• Figure 7: Quasiparticle heating over time for $N=7$ without loss.