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Creating big time crystals with ultracold atoms

Krzysztof Giergiel, Krzysztof Sacha, Tien Tran, Ali Zaheer, Andrei I. Sidorov, Peter Hannaford

Published Dec 30, 2019• 0 citations
Publisher

Abstract

We report progress towards realizing discrete time crystals using a BEC of potassium-39 atoms bouncing on an oscillating mirror. In the absence of interactions, each bouncing atom performs classical motion in which there are resonant islands in phase space located around periodic orbits whose periods match an integral multiple s of the driving period T of the mirror. If all the atoms are prepared in a single wave-packet, in the absence of interactions they tunnel to neighbouring wave-packets on a timescale determined by the driving amplitude and period of the oscillating mirror. In the presence of a sufficiently strong attractive interaction, the Floquet eigenstates of the periodic system become Schrödinger cat-like states, so that measurement of the position of just a single atom is sufficient to break the timetranslation symmetry and cause the system to collapse into one of the s wave-packets bouncing with period sT. Such a system allows dramatic breaking of discrete time translation symmetry where the symmetry-broken state evolves with a period typically s=40 times longer than the driving period and does not decay. This system provides also a suitable platform for demonstrating a wide range of condensed matter phenomena in the time domain.

DOI
10.1117/12.2539858

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We report progress towards realizing discrete time crystals using a BEC of potassium-39 atoms bouncing on an oscillating mirror. In the absence of interactions, each bouncing atom performs classical motion in which there are resonant islands in phase space located around periodic orbits whose periods match an integral multiple s of the driving period T of the mirror. If all the atoms are prepared in a single wave-packet, in the absence of interactions they tunnel to neighbouring wave-packets on a timescale determined by the driving amplitude and period of the oscillating mirror. In the presence of a sufficiently strong attractive interaction, the Floquet eigenstates of the periodic system become Schrödinger cat-like states, so that measurement of the position of just a single atom is sufficient to break the timetranslation symmetry and cause the system to collapse into one of the s wave-packets bouncing with period sT. Such a system allows dramatic breaking of discrete time translation symmetry where the symmetry-broken state evolves with a period typically s=40 times longer than the driving period and does not decay. This system provides also a suitable platform for demonstrating a wide range of condensed matter phenomena in the time domain.
Abstract We investigate the size of discrete time crystals s (ratio of response period to driving period) that can be created for a Bose–Einstein condensate (BEC) bouncing resonantly on an oscillating mirror. We find that time crystals can be created with sizes in the range s ≈ 20–100 and that such big time crystals are easier to realize experimentally than a period-doubling (s=2) time crystal because they require either a larger drop height or a smaller number of bounces on the mirror. We also investigate the effects of having a realistic soft Gaussian potential mirror for the bouncing BEC, such as that produced by a repulsive light-sheet, which is found to make the experiment easier to implement than a hard-wall potential mirror. Finally, we discuss the choice of atomic system for creating time crystals based on a bouncing BEC and present an experimental protocol for realizing big time crystals. Such big time crystals provide a flexible platform for investigating a broad range of non-trivial condensed matter phenomena in the time domain.
Time crystals are quantum many-body systems which are able to self-organize their motion in a periodic way in time. Discrete time crystals have been experimentally demonstrated in spin systems. However, the first idea of spontaneous breaking of discrete time translation symmetry, in ultracold atoms bouncing on an oscillating mirror, still awaits experimental demonstration. Here, we perform a detailed analysis of the experimental conditions needed for the realization of such a discrete time crystal. Importantly, the considered system allows for the realization of dramatic breaking of discrete time translation symmetry where a symmetry broken state evolves with a period tens of times longer than the driving period. Moreover, atoms bouncing on an oscillating mirror constitute a suitable system for the realization of dynamical quantum phase transitions in discrete time crystals and for the demonstration of various nontrivial condensed-matter phenomena in the time domain. We show that Anderson localization effects, which are typically associated with spatial disorder and exponential localization of eigenstates of a particle in configuration space, can be observed in the time domain when ultracold atoms are bouncing on a randomly moving mirror.
Abstract We review the application of discrete time crystals created in a Bose-Einstein condensate (BEC) of ultracold atoms bouncing resonantly on an oscillating atom mirror to the investigation of condensed matter phenomena in the time dimension. Such a bouncing BEC system can exhibit dramatic breaking of time-translation symmetry, allowing the creation of discrete time crystals having up to about 100 temporal lattice sites and suitable for hosting a broad range of temporal condensed matter phenomena. We first consider single-particle condensed matter phenomena in the time dimension which include Anderson localization due to temporal disorder, topological time crystals, and quasi-crystal structures in time. We then discuss many-body temporal condensed matter phenomena including Mott insulator phases in time, many-body localization in time, many-body topological time crystals and time crystals having long-range exotic interactions. We also discuss the construction of two (or three) dimensional time lattices, involving the bouncing of a BEC between two (or three) orthogonal oscillating mirrors and between two oscillating mirrors oriented at 45∘. The latter configuration supports a versatile Möbius strip geometry which can host a variety of two-dimensional time lattices including a honeycomb time lattice and a Lieb square time lattice. Finally, we discuss the construction of a six-dimensional time-space lattice based on periodically driven BECs trapped in a three-dimensional optical lattice.
Time crystals are quantum systems that are able to reveal condensed matter behavior in the time domain. It is known that crystallization in time can be observed in a periodically driven many-body system when interactions between particles force a system to evolve with a period that is an integer multiple of a driving period. This phenomenon is dubbed discrete time crystal formation. Here, we consider ultracold atoms bouncing on an oscillating atom mirror and show that the system can spontaneously form a discrete time crystal where the ratio of a period of its motion and a driving period is a rational number. This kind of discrete time crystal requires higher-order resonant driving, which is analyzed here with the help of an original approach.
Abstract We study discrete time crystal (DTC) formation in a system driven periodically by an oscillating atomic mirror, consisting of two distinct ultracold atomic clouds in the presence of a gravitational field. The intra-species interactions are weak and attractive, while the inter-species interactions are infinitely strong and repulsive. The clouds are arranged in a one-dimensional stack, where the bottom cloud bounces on an oscillating atomic mirror, which effectively acts as a driving force for the upper cloud due to the infinite inter-species repulsion. Using a Jastrow-like variational ansatz for the many-body wavefunction, we show numerically that sufficiently strong attractive intra-species interactions drive each subsystem to spontaneously break discrete time translation symmetry, resulting in the formation of a cascading DTC evolving with a period different than the driving period. Since the bottom cloud serves as the effective periodic driving for the upper cloud, this leads to a cascade of spontaneous symmetry breaking. With increasing intra-species interactions, we first observe a pronounced effect of spontaneous time translation symmetry breaking in the upper cloud, followed by a similar effect in the lower atomic cloud.
Despite being forbidden in equilibrium, spontaneous breaking of time translation symmetry can occur in periodically driven, Floquet systems with discrete time-translation symmetry.The period of the resulting discrete time crystal is quantized to an integer multiple of the drive period, arising from a combination of collective synchronization and many body localization.Here, we consider a simple model for a onedimensional discrete time crystal which explicitly reveals the rigidity of the emergent oscillations as the drive is varied.We numerically map out its phase diagram and compute the properties of the dynamical phase transition where the time crystal melts into a trivial Floquet insulator.Moreover, we demonstrate that the model can be realized with current experimental technologies and propose a blueprint based upon a one dimensional chain of trapped ions.Using experimental parameters (featuring long-range interactions), we identify the phase boundaries of the ion-time-crystal and propose a measurable signature of the symmetry breaking phase transition.