Quantum technologies exploit entanglement to revolutionize computing, measurements, and communications. This has stimulated the research in different areas of physics to engineer and manipulate fragile many-particle entangled states. Progress has been particularly rapid for atoms. Thanks to the large and tunable nonlinearities and the well-developed techniques for trapping, controlling, and counting, many groundbreaking experiments have demonstrated the generation of entangled states of trapped ions, cold, and ultracold gases of neutral atoms. Moreover, atoms can strongly couple to external forces and fields, which makes them ideal for ultraprecise sensing and time keeping. All these factors call for generating nonclassical atomic states designed for phase estimation in atomic clocks and atom interferometers, exploiting many-body entanglement to increase the sensitivity of precision measurements. The goal of this article is to review and illustrate the theory and the experiments with atomic ensembles that have demonstrated many-particle entanglement and quantum-enhanced metrology.

Quantum metrology with nonclassical states of atomic ensembles

Adiabatic evolution along the instantaneous eigenstate of a time-dependent Hamiltonian is used for robust and high fidelity state transfer in atomic and molecular physics. Shortcuts to adiabaticity (STA) are systematic approaches to accomplish the same final state transfer in a faster manner. This article presents an introduction to STA and reviews different theoretical approaches and applications of STA to a range of scientific and engineering tasks in quantum physics and beyond.

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Shortcuts to adiabaticity: Concepts, methods, and applications

It is control that turns scientific knowledge into useful technology: in physics and engineering it provides a systematic way for driving a dynamical system from a given initial state into a desired target state with minimized expenditure of energy and resources As one of the cornerstones for enabling quantum technologies, optimal quantum control keeps evolving and expanding into areas as diverse as quantum-enhanced sensing, manipulation of single spins, photons, or atoms, optical spectroscopy, photochemistry, magnetic resonance (spectroscopy as well as medical imaging), quantum information processing and quantum simulation In this communication, state-of-the-art quantum control techniques are reviewed and put into perspective by a consortium of experts in optimal control theory and applications to spectroscopy, imaging, as well as quantum dynamics of closed and open systems We address key challenges and sketch a roadmap for future developments

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Training Schrödinger’s cat: quantum optimal control

Quantum adiabatic processes--that keep constant the populations in the instantaneous eigenbasis of a time-dependent Hamiltonian--are very useful to prepare and manipulate states, but take typically a long time. This is often problematic because decoherence and noise may spoil the desired final state, or because some applications require many repetitions. "Shortcuts to adiabaticity" are alternative fast processes which reproduce the same final populations, or even the same final state, as the adiabatic process in a finite, shorter time. Since adiabatic processes are ubiquitous, the shortcuts span a broad range of applications in atomic, molecular, and optical physics, such as fast transport of ions or neutral atoms, internal population control, and state preparation (for nuclear magnetic resonance or quantum information), cold atom expansions and other manipulations, cooling cycles, wavepacket splitting, and many-body state engineering or correlations microscopy. Shortcuts are also relevant to clarify fundamental questions such as a precise quantification of the third principle of thermodynamics and quantum speed limits. We review different theoretical techniques proposed to engineer the shortcuts, the experimental results, and the prospects.

http://www.spindynamics.org/documents/conf/QUAINT2013/QUAINT2013_muga.pdf

Shortcuts to Adiabaticity

The description of the non-equilibrium dynamics of isolated quantum many-body systems within the framework of statistical mechanics is a fundamental open question. Conventional thermodynamical ensembles fail to describe the large class of systems that exhibit nontrivial conserved quantities, and generalized ensembles have been predicted to maximize entropy in these systems. We show experimentally that a degenerate one-dimensional Bose gas relaxes to a state that can be described by such a generalized ensemble. This is verified through a detailed study of correlation functions up to 10th order. The applicability of the generalized ensemble description for isolated quantum many-body systems points to a natural emergence of classical statistical properties from the microscopic unitary quantum evolution.

https://science.sciencemag.org/content/sci/348/6231/207.full.pdf

Experimental Observation of a Generalized Gibbs Ensemble

Particle-wave duality enables the construction of interferometers for matter waves, which complement optical interferometers in precision measurement devices. This requires the development of atom-optics analogues to beam splitters, phase shifters and recombiners. Integrating these elements into a single device has been a long-standing goal. Here we demonstrate a full Mach-Zehnder sequence with trapped Bose-Einstein condensates confined on an atom chip. Particle interactions in our Bose-Einstein condensate matter waves lead to a nonlinearity, absent in photon optics. We exploit it to generate a non-classical state having reduced number fluctuations inside the interferometer. Making use of spatially separated wave packets, a controlled phase shift is applied and read out by a non-adiabatic matter-wave recombiner. We demonstrate coherence times a factor of three beyond what is expected for coherent states, highlighting the potential of entanglement as a resource for metrology. Our results pave the way for integrated quantum-enhanced matter-wave sensors.

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Integrated Mach–Zehnder interferometer for Bose–Einstein condensates

We present an investigation of the fast decompression of a three-dimensional (3D) Bose-Einstein condensate (BEC) at finite temperature using an engineered trajectory for the harmonic trapping potential. Taking advantage of the scaling invariance properties of the time-dependent Gross-Pitaevskii equation, we exhibit a solution yielding a final state identical to that obtained through a perfectly adiabatic transformation, in a much shorter time. Experimentally, we perform a large trap decompression and displacement within a time comparable to the final radial trapping period. By simultaneously monitoring the BEC and the non-condensed fraction, we demonstrate that our specific trap trajectory is valid both for a quantum interacting many-body system and a classical ensemble of non-interacting particles.

http://iopscience.iop.org/article/10.1209/0295-5075/93/23001/pdf

Shortcut to adiabaticity for an interacting Bose-Einstein condensate

We demonstrate a technique based on invariants of motion for a time-dependent Hamiltonian, allowing a fast transition to a final state identical in theory to that obtained through a perfectly adiabatic transformation. This method is experimentally applied to the fast decompression of an ultracold cloud of $^{87}\mathrm{Rb}$ atoms held in a harmonic magnetic trap in the presence of gravity. We are able to decompress the trap by a factor of $15$ within $35$ ms with a strong suppression of the sloshing and breathing modes induced by the large vertical displacement and curvature reduction of the trap. When compared to a standard linear decompression, we achieve a gain of a factor of $37$ on the transition time.

Fast optimal transition between two equilibrium states

We study experimentally and theoretically the controlled transfer of harmonically trapped ultracold gases between different quantum states. In particular, we experimentally demonstrate a fast decompression and displacement of both a non-interacting gas and an interacting Bose–Einstein condensate, which are initially at equilibrium. The decompression parameters are engineered such that the final state is identical to that obtained after a perfectly adiabatic transformation despite the fact that the fast decompression is performed in the strongly non-adiabatic regime. During the transfer the atomic sample goes through strongly out-of-equilibrium states, while the external confinement is modified until the system reaches the desired stationary state. The scheme is theoretically based on the invariants of motion and scaling equation techniques and can be generalized to decompression trajectories including an arbitrary deformation of the trap. It is also directly applicable to arbitrary initial non-equilibrium states.

http://iopscience.iop.org/article/10.1088/1367-2630/13/11/113017/pdf

Shortcuts to adiabaticity for trapped ultracold gases

The Ramsey interferometer is a prime example of precise control at the quantum level. It is usually implemented using internal states of atoms, molecules or ions, for which powerful manipulation procedures are now available. Whether it is possible to control external degrees of freedom of more complex, interacting many-body systems at this level remained an open question. Here we demonstrate a two-pulse Ramsey-type interferometer for non-classical motional states of a Bose–Einstein condensate in an anharmonic trap. The control sequences used to manipulate the condensate wavefunction are obtained from optimal control theory and are directly optimized to maximize the interferometric contrast. They permit a fast manipulation of the atomic ensemble compared to the intrinsic decay processes and many-body dephasing effects. This allows us to reach an interferometric contrast of 92% in the experimental implementation.

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Jean-François Schaff

Papers

Integrated Mach–Zehnder interferometer for Bose–Einstein condensates

Shortcut to adiabaticity for an interacting Bose-Einstein condensate

Fast optimal transition between two equilibrium states

Shortcuts to adiabaticity for trapped ultracold gases

Interferometry with non-classical motional states of a Bose-Einstein condensate