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We propose a method to produce a definite number of ground-state atoms by adiabatic reduction of the depth of a potential well that confines a degenerate Bose gas with repulsive interactions. Using a variety of methods, we map out the maximum number of particles that can be supported by the well as a function of the well depth and interaction strength, covering the limiting case of a Tonks gas as well as the mean-field regime. We also estimate the time scales for adiabaticity and discuss the recent observation of atomic number squeezing (Chuu et al., Phys. Rev. Lett. {bf 95}, 260403 (2005)).
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Certain wave functions of non-interacting quantum chaotic systems can exhibit scars in the fabric of their real-space density profile. Quantum scarred wave functions concentrate in the vicinity of unstable periodic classical trajectories. We introduce the notion of many-body quantum scars which reflect the existence of a subset of special many-body eigenstates concentrated in certain parts of the Hilbert space. We demonstrate the existence of scars in the Fibonacci chain -- the one- dimensional model with a constrained local Hilbert space realized in the 51 Rydberg atom quantum simulator [H. Bernien et al., arXiv:1707.04344]. The quantum scarred eigenstates are embedded throughout the thermalizing many-body spectrum, but surprisingly lead to direct experimental signatures such as robust oscillations following a quench from a charge-density wave state found in experiment. We develop a model based on a single particle hopping on the Hilbert space graph, which quantitatively captures the scarred wave functions up to large systems of L = 32 atoms. Our results suggest that scarred many-body bands give rise to a new universality class of quantum dynamics, which opens up opportunities for creating and manipulating novel states with long-lived coherence in systems that are now amenable to experimental study.
Quantum batteries are quantum mechanical systems with many degrees of freedom which can be used to store energy and that display fast charging. The physics behind fast charging is still unclear. Is this just due to the collective behavior of the underlying interacting many-body system or does it have its roots in the quantum mechanical nature of the system itself? In this work we address these questions by studying three examples of quantum-mechanical many-body batteries with rigorous classical analogs. We find that the answer is model dependent and, even within the same model, depends on the value of the coupling constant that controls the interaction between the charger and the battery itself.
We analyse the properties of the synchronisation transition in a many-body system consisting of quantum van der Pol oscillators with all-to-all coupling using a self-consistent mean-field method. We find that the synchronised state, which the system can access for oscillator couplings above a critical value, is characterised not just by a lower phase uncertainty than the corresponding unsynchronised state, but also a higher number uncertainty. Just below the critical coupling the system can evolve to the unsynchronised steady state via a long-lived transient synchronised state. We investigate the way in which this transient state eventually decays and show that the critical scaling of its lifetime is consistent with a simple classical model.
Achieving high-precision detection of time-dependent signals in noisy environment is a ubiquitous issue in physics and a critical task in metrology. Lock-in amplifiers are detectors that can extract alternating signals with a known carrier frequency from an extremely noisy environment. Here, we present a protocol for achieving an entanglement-enhanced lock-in amplifier via empoying many-body quantum interferometry and periodic multiple pulses. Generally, quantum interferometry includes three stages: initialization, interrogation, and readout. The many-body quantum lock-in amplifier can be achieved via adding suitable periodic multiple-$pi$-pulse sequence during the interrogation. Our analytical results show that, by selecting suitable input states and readout operations, the frequency and amplitude of an unknown alternating field can be simultaneously extracted via population measurements. In particular, if we input spin cat states and apply interaction-based readout operations, the measurement precisions for frequency and amplitude can both approach the Heisenberg limit. Moreover, our many-body quantum amplifier is robust against extreme stochastic noises. Our study may point out a new direction for measuring time-dependent signals with many-body quantum systems, and provides a feasible way for achieving Heisenberg-limited detection of alternating signals.
The spectral form factor (SFF), characterizing statistics of energy eigenvalues, is a key diagnostic of many-body quantum chaos. In addition, partial spectral form factors (pSFFs) can be defined which refer to subsystems of the many-body system. They provide unique insights into energy eigenstate statistics of many-body systems, as we show in an analysis on the basis of random matrix theory and of the eigenstate thermalization hypothesis. We propose a protocol which allows the measurement of SFF and pSFFs in quantum many-body spin models, within the framework of randomized measurements. Aimed to probe dynamical properties of quantum many-body systems, our scheme employs statistical correlations of local random operations which are applied at different times in a single experiment. Our protocol provides a unified testbed to probe many-body quantum chaotic behavior, thermalization and many-body localization in closed quantum systems which we illustrate with simulations for Hamiltonian and Floquet many-body spin-systems.
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