Semiclassical wave packet dynamics in quantum systems with loss and gain
While traditional quantum mechanics focusses on systems conserving energy and probability, described by Hermitian Hamiltonians, in recent years there has been ever growing interest in the use of non-Hermitian Hamiltonians. These can effectively describe loss and gain in a quantum system. In particular systems with a certain balance of loss and gain, so-called PT-symmetric systems, have attracted considerable attention. The realisation of PT-symmetric quantum dynamics in optical systems has opened up a whole new field of investigations.
In Hermitian systems, the dynamics of wave packets, which for short times reduces to classical dynamics, provide important insights and tools for quantitative simulations of quantum dynamics. Recently a semiclassical limit of non-Hermitian quantum mechanics has been proposed that allows for a similar description of quantum dynamics generated by non-Hermitian Hamiltonians on the grounds of classical phase-space trajectories. In this talk it will be demonstrated that this classical dynamics can describe the main features of the propagation of optical beams in the presence of gain and loss. We consider two main applications, the propagation of Gaussian beams in a multi-mode wave guide with gain and loss, and Bloch oscillations in a non-Hermitian tight-binding lattice.
Spin dynamics of individual neutral impurities in a Bose-Einstein condensate
Individual spins immersed into a superfluid form a paradigm of quantum physics. It lies at the heart of many models exploiting the quantum nature of individual spins to understand quantum phenomena or to open novel routes to local probing and engineering of quantum many-body systems.
I will present our approach of controlled immersion of individual, localized neutral Caesium (Cs) atoms having total spin F = 3 into a Rubidium Bose-Einstein condensate (BEC) with total spin F = 1. Depending on the Zeeman-state of the Rb gas, we observe inelastic spin-exchange dynamics, tracing the spin state of individual impurities with high position and time resolution. Moreover, suppressing such inelastic collisions by proper choice of internal states, we demonstrate coherent dynamics of individual Cs impurities’ quasi-spins immersed in the BEC.Our work paves the way for local quantum probing of superfluids, and thus might shed light on the local state of nonequilibrium or correlated quantum many-body systems.
Event-ready loophole free Bell tests - From Foundations to Applications
An experimental test of Bell's inequality allows to test the validity of local-realistic descriptions of nature by measuring correlations between distant systems. While such tests are conceptually simple, there are strict requirements concerning the detection efficiency of the involved measurements, as well as the enforcement of space-like separation between the measurement events. Only recently both loopholes could be closed simultaneously.
Here we present our approach based on combining heralded entanglement of atoms separated by 398 m with fast and efficient measurements of the atomic spin states. We obtain a violation S=2.22 +/ 0.033 > 2, which allows us to refute the hypothesis of local-realism with very high significance.
The mere fact that the existence of local hidden variables, i.e. inforamtion about the state, can be tested enables one to design protocols in quantum communication testing the existence of any possible information an eavesdropper could have about the communication. We discuss the benefits and requirements for the experiment of such so called device independent communication schemes.
The method to generate entanglement between remote quantum systems forms the core ingredient for quantum repeater. Starting from the present experiment, we also discuss the prospects and roadmaps towards future quantum networks.
Optical fiber-based quantum communication
The ultimate goal of quantum communication is to form high-quality entanglement between quantum memories located far away. For this purpose, there is no choice but to use photons as the quantum information careers. An optical fiber or a free-space optical beam will be used as the optical transmission line. We are focusing on "entanglement formation between distant quantum memories" using optical fibers. The main challenges are (1) correction of quantum errors of photons that are induced during photon propagation through a long-haul fiber, and (2) transferring the quantum information of a memory --- which does not interact with the telecom photons --- to the telecom photons.
As for problem (1), quantum error correction code is not suited to long-range quantum communication because the probability that all n (>= 5) photons that are used to encode one logical qubit survive becomes unrealistically small. Fortunately, the fluctuation of the optical fiber is slow enough so the errors that are brought to the photons are not independent but correlated, that is, the noise is so called "collective noise." In this case, n can be reduced, and in our study we could reduce n to 2, and finally to 1! In the early stage of our research, bit errors were not corrected but only the phase errors. Finally, however, we could correct not only the phase errors but also the bit errors, keeping n=1. With this, we were able to settle the problem (1).
For challenge (2), we developed wavelength conversion technology. Here, the wavelength conversion is not the conventional ones but such a type that does not destroy the entanglement. The key element for this is coherent wavelength conversion (both down-conversion and up-conversion). Using Type-0 phase-matched nonlinear optics, we have realized this by designing PPLNs (periodically-poled LiNbO3). Currently the conversion efficiency (the probability of not losing the photon) is about 70%, but this value is expected to reach nearly 100% in the near future.
Another important elements are high quality photon detectors, namely, SSPDs (superconducting single-photon detectors). SSPDs have advantage not only that they can detect telecom photons, but also that their performance is much improved than the conventional detectors, for instance, they have low jitters. When conventional detectors are used, the measured entanglement is statistically estimated much lower than its real amount due to jitters, etc., even though the wavelength converter itself is in the quantum region. In this case, the total system is evaluated to be "classical." Using SSPDs, however, it became possible to evaluate the entanglement correctly.
And finally, we came to the stage of "transferring quantum state of real memory to/from telecom photons." Here we use the ensemble of Rb atoms. We feel that our research is now close to "formation of entanglement between far distant memories using long-haul optical fibers.”
Optimized STIRAP-type State Transfer in Solid-State Quantum Devices
Great improvements in the coherent control of solid-state devices has led to remarkable demonstrations of STIRAP in superconducting qubits, optomechanical systems, NV centers, and so on. However, differently from atomic systems, most solid-state quantum devices suffer significant dissipation, thus the prolonged operation time of STIRAP (required by adiabaticity) becomes a severe drawback. In these examples the trade-off between adiabaticity and decoherence is a central issue, which has been investigated numerically but no analytical conclusion has been made. In order to provide physical insight and understand the power of STIRAP in the realistic scenario, we have pursued an analytical treatment with full consideration of the system dissipation. We find that optimizing the transfer time rather than coupling profiles leads to a significant improvement of the transfer fidelity. The upper bound of the fidelity has been found as a simple analytical function of system cooperativities. We also provide a systematic approach to reach this upper bound efficiently. By including the dissipation of all the parties, our results are widely applicable to quantum state engineering and are particularly relevant for solid-state devices.
Entanglement field theories - a new approach to experimentally measure and theoretically understand entanglement in many-body systems
In this talk, I will discuss how interpreting the reduced density matrix of a system bipartition opens new routes to understand entanglement properties of many-body quantum systems both at the experimental and theoretical level. Firstly, I will discuss an approach to directly measure eigenvalues of reduced density matrices - the so called ‘entanglement’ spectrum - using a direct spectroscopy of the entanglement Hamiltonian. Contrary to tomographic techniques, this approach is based upon conventional spectroscopy, and is thus immediately scalable to many-body systems with 100+ degrees of freedom. A short overview of some concrete experimental implementations, including both atomic and solid state systems, will be provided. Secondly, I will discuss advantages and limitations of interpreting reduced density matrices as effective partition functions. These theoretical results are not only important to design novel probes for entanglement, but, most importantly, provide a new perspective to characterize entanglement (and complexity of wave functions) using techniques and concepts from statistical mechanics and field theory.
Dynamics of impurities in quantum gases
The behaviour of a mobile impurity particle interacting with a quantum-mechanical medium is of fundamental importance in physics. Ultracold atomic gases have greatly improved our understanding of the impurity problem owing to the high degree of control over experimental parameters such as interactions and atom population. I will discuss recent theoretical and experimental progress in exploring the properties of impurities interacting with bosonic and fermonic mediums. In particular, I will introduce a new theoretical approach for describing the coherent non-perturbative quantum evolution following a quench of the impurity-medium interactions [1,2].
 M. Cetina et al., Science 354, 96 (2016).
 M. M. Parish and J. Levinsen, Phys. Rev. B 94, 184303 (2016).
Time crystals in strongly interacting dipolar spin systems
The interplay between periodic driving, disorder, and strong interactions has been predicted to result in exotic time crystalline phases, which spontaneously break the discrete time-translation symmetry of the underlying drive. In this talk, I will present the experimental observation of such discrete time crystalline order in a driven, disordered ensemble of about one million dipolar spin impurities in diamond at room temperature. We observe long-lived temporal correlations, experimentally identify the phase boundary and find that the temporal order is protected by strong interactions. We quantitatively explain these observations using resonance counting, which reveals critically slow thermalization dynamics as the origin of the observed long lived order.
Holonomic quantum control of hybrid spin qubits in an NV center in diamond
Realization of fast fault-tolerant quantum gates on a single spin is the core requirement for solid-state quantum-information processing. As a polarized light shows geometric interference, a spin coherence is geometrically controlled with light via the spin-orbit interaction or directly with microwave. We show that a geometric spin in a degenerate subspace of a spin-1 electronic system in the nitrogen vacancy center in diamond allows implementation of optical non-adiabatic holonomic quantum gates. We also demonstrate the universal quantum holonomic gates on electron-nuclear hybrid spin system with polarized microwaves. The optical holonomic quantum gates open the way towards holonomic quantum computers and repeaters.
Atomic Spin Entanglement and Anyonic Fractional Statistics in an Optical Lattice
In this talk, I will report our recent research progress with ultracold atoms trapped in optical lattices. Ultracold atoms in optical lattices hold promise for the creation of entangled states for quantum simulation and quantum computation. In our experiment, we developed a novel setup of spin-dependent optical superlattice. We were able to generate, manipulate and detect the atomic spin entanglement in this lattice. Moreover, based on the techniques of precisely manipulating atomic spins, we built a minimum version of the toric code Hamiltonian with four atomic spins in optical plaquettes. We observed four-body ring-exchange interactions, existing in many-body systems while never observed before in experiment, and the topological properties of anyonic excitations within this ultracold atom system. This work represents an essential step towards studying topological matters with ultracold atoms and offers new perspectives on topological quantum simulation.
Quantum engineering using magnetic fields: Quantum Magnetomechanics
Optomechanics - the control and manipulation of mesocopic objects towards the quantum regime, has attracted much attention. The use of light however, brings with it several problems, scattering noise being just one. In this talk we introduce a new approach to control the quantum motion of mescoscopic objects using magnetic fields. We describe a proposal to levitate and cool superconducting objects using magnetic fields and superconducting quantum circuits, how such levitated objects can be used for high precision gravimetry, how one can engineer spin entanglement and how this can be developed into a quantum computer architecture. We outline preliminary experimental results in magentomechanical levitation and cooling of small micron sized particles.
Engineering the quantum spin dynamics of donors in silicon
Spins in silicon offer a rich playground for the study of correlated systems and many-body interactions, combined with coherence times ranging up to seconds (electron spins) and hours (nuclear spins). Donor spins have been used as probes to study the dynamics of the surrounding nuclear spin bath, and the nature of this bath has been shown to change when tuning the donor spin to/from magnetic-field-insensitive “clock transitions”. Using bismuth donors coupled to superconducting cavities, cavity-induced spin relaxation has been observed for the first time, and electron spin resonance (ESR) of donors in silicon has been performed using squeezed microwaves, enabling ESR beyond the standard quantum limit of sensitivity.
Finally, phosphorus donor spins have been used to study discrete time-crystalline behaviour.
The Search for a QBist Formulation of Quantum Control
Steven Weinberg once wrote an article for the New York Review of Books titled, “Symmetry: A `Key to Nature’s Secrets’.” So too, the Quantum Bayesians, or QBists, would like to say of quantum theory itself: Only by identifying Hilbert space’s most hard-to-get symmetries will we be able to unlock quantum theory’s deepest secrets and greatest potential. In this talk, I introduce the “symmetric informationally complete” (SIC) sets of quantum states as a candidate for such a symmetry. When these structures exist—and it seems they do for all finite dimensions, though in 18 years of effort no one has yet proven it—one can use them to re-express a quantum state as a single probability distribution and a unitary transformation as a single doubly stochastic matrix. Most importantly, this formalism gives an insightful way to rewrite both the Born rule and the time-integrated Schroedinger equation in purely probabilistic terms, never once mentioning operators or Hilbert space. Indeed, what is intriguing is the way both these formulas become visually similar to the classical law of total probability and the classical expression for stochastic time evolution. In fact one can prove rigorously that, of all probabilistic representations of the Born rule, the version in terms of the SICs brings it as close to the classical law as it can ever be, under nearly every known measure of “close” (Frobenius norm, trace norm, Schatten p-norms, Ky Fan k-norms, etc.). This suggests the SIC representation as a natural starting point for elucidating the minimal difference between quantum control and classical stochastic control, and has the potential to bring the vast toolbox of classical control theory more easily to bear upon its quantum counterpart.