Recent experimental realizations of uniform confining potentials for ultracold atoms make it possible to create quantum acoustic resonators and explore nonequilibrium dynamics of quantum field theories. These systems offer a promising new platform fo
r studying the dynamical Casimir effect, since they allow to achieve relativistic, i.e. near sonic, velocities of the boundaries. In comparison to previously studied optical and classical hydrodynamic systems ultracold atoms allow to realize a broader class of dynamical experiments combining both classical driving and vacuum squeezing. In this paper we discuss theoretically two types of experiments with interacting one dimensional condensates with moving boundaries. Our analysis is based on the Luttinger liquid model which utilizes the emergent conformal symmetry of the low energy sector of the Lieb-Liniger model. The first system we consider is a variable length interferometer with two Y-junctions connected back to back. We demonstrate that dynamics of the relative phase between the two arms of the interferometer can be analyzed using the formalism developed by Moore in the problem of electromagnetic vacuum squeezing in a cavity with moving mirrors. The second system we discuss is a single condensate in a box potential with periodically moving walls. This system exhibits classical excitation of the mode resonant with the drive as well as nonlinear generation of off-resonant modes. In addition we find strong parametric multimode squeezing between modes whose energy difference matches integer multiples of the drive frequency.
In this chapter we will present the one-dimensional (1d) quantum degenerate Bose gas (1d superfluid) as a testbed to experimentally illustrate some of the key aspects of quantum thermodynamics. Hard-core bosons in one-dimension are described by the i
ntegrable Lieb-Lininger model. Realistic systems, as they can be implemented, are only approximately integrable, and let us investigate the cross over to thermalisation. They show such fundamental properties as pre-thermalisation, general Gibbs ensembles and light-cone like spreading of de-coherence. On the other hand they are complex enough to illustrate that our limited ability to measure only (local) few-body observables determines the relevant description of the many-body system and its physics. One consequence is the observation of quantum recurrences in systems with thousand of interacting particles. The relaxation observed in 1D superfluids is universal for a large class of many-body systems, those where the relevant physics can be described by a set of long lived collective modes. The time window where the close to integrable dynamics can be observed is given by the lifetime of the quasi-particles associated with the collective modes. Based on these observations one can view (in a quantum field theory sense) a many-body quantum system at T=0 as vacuum and its excitations as the system to experiment with. This viewpoint leads to a new way to build thermal machines from the quasi-particles in 1D superfluids. We will give examples of how to realise these systems and point to a few interesting questions that might be addressed.
We theoretically analyze a Mach-Zehnder interferometer with trapped condensates, and find that it is surprisingly stable against the nonlinearity induced by inter-particle interactions. The phase sensitivity, which we study for number squeezed input
states, can overcome the shot noise limit and be increased up to the Heisenberg limit provided that a Bayesian or Maximum-Likelihood phase estimation strategy is used. We finally demonstrate robustness of the Mach-Zehnder interferometer in presence of interactions against condensate oscillations and a realistic atom counting error.
Interferometry with ultracold atoms promises the possibility of ultraprecise and ultrasensitive measurements in many fields of physics, and is the basis of our most precise atomic clocks. Key to a high sensitivity is the possibility to achieve long m
easurement times and precise readout. Ultra cold atoms can be precisely manipulated at the quantum level, held for very long times in traps, and would therefore be an ideal setting for interferometry. In this paper we discuss how the non-linearities from atom-atom interactions on one hand allow to efficiently produce squeezed states for enhanced readout, but on the other hand result in phase diffusion which limits the phase accumulation time. We find that low dimensional geometries are favorable, with two-dimensional (2D) settings giving the smallest contribution of phase diffusion caused by atom-atom interactions. Even for time sequences generated by optimal control the achievable minimal detectable interaction energy $Delta E^{rm min}$ is on the order of 0.001 times the chemical potential of the BEC in the trap. From there we have to conclude that for more precise measurements with atom interferometers more sophisticated strategies, or turning off the interaction induced dephasing during the phase accumulation stage, will be necessary.
We theoretically analyze atom interferometry based on trapped ultracold atoms, and employ optimal control theory in order to optimize number squeezing and condensate trapping. In our simulations, we consider a setup where the confinement potential is
transformed from a single to a double well, which allows to split the condensate. To avoid in the ensuing phase-accumulation stage of the interferometer dephasing due to the nonlinear atom-atom interactions, the atom number fluctuations between the two wells should be sufficiently low. We show that low number fluctuations (high number squeezing) can be obtained by optimized splitting protocols. Two types of solutions are found: in the Josephson regime we find an oscillatory tunnel control and a parametric amplification of number squeezing, while in the Fock regime squeezing is obtained solely due to the nonlinear coupling, which is transformed to number squeezing by peaked tunnel pulses. We study splitting and squeezing within the frameworks of a generic two-mode model, which allows us to study the basic physical mechanisms, and the multi-configurational time dependent Hartree for bosons method, which allows for a microscopic modeling of the splitting dynamics in realistic experiments. Both models give similar results, thus highlighting the general nature of these two solution schemes. We finally analyze our results in the context of atom interferometry.
We optimize number squeezing when splitting a mesoscopic Bose Einstein condensate. Applying optimal control theory to a realistic description of the condensate allowed us to identify a form of the splitting ramp which drastically outperforms the adia
batic splitting. The results can be interpreted in terms of a generic two-mode model mapped onto a parametric harmonic oscillator. This optimal route to squeezing paves the way to a much longer phase coherence and atom interferometry close to the Heisenberg limit.
By placing changeable nanofabricated structures (wires, dots, etc.) on an atom mirror one can design guiding and trapping potentials for atoms. These potentials are similar to the electrostatic potentials which trap and guide electrons in semiconduct
or quantum devices like quantum wires and quantum dots. This technique will allow the fabrication of nanoscale atom optical devices.
