Quantum Sensing with Quantum Correlated Systems

Entanglement has grown from a quantum curiosity into a cornerstone of modern quantum theory, and acts as a resource in future quantum technologies such as quantum metrology. I will describe how opticql fiber microcavities can be used to produce and detect multiparticle entanglement in ultracold atoms, and show examples from recent experiments in our group. I will also describe progress towards a spin-squeezed atomic clock on a chip using these devices.

In the quest to approach the Heisenberg limit in precision measurements, noise and dissipation are formidable adversaries. I will describe two strategies for minimizing their detrimental impact in the generation and detection of metrologically useful entangled states, including over-squeezed non-Gaussian states and Schrödinger cat states. While focusing on prospects for harnessing these strategies in cavity-QED experiments with many atoms strongly coupled to a single mode of light, I will also touch on prospective extensions to quantum sensing in a variety of other platforms.

Change point detection is a pivotal task is statistical analysis that aims at identifying the moment when a sequence of observed data changes its underlying probability distribution. We study the quantum extension of this problem where a source emits quantum particles in a default state, until a point where a mutation occurs that causes the source to produce a different state. The problem is then to find out where the change occurred. We determine the optimal strategy for the correct identification of the change point with minimum error probability, as well as for the unambiguous identification, where the change point is identified with certainty ---at the price of getting an inconclusive answer with some non-vanishing probability. We also discuss local (online) protocols and compare them with the optimal procedures.

Quantum correlated states are a key resource to improve the sensitivity of interferometers beyond the standard quantum limit. In the context of magnetic sensing by an assembly of atoms or ions, paradigmatic examples are represented by spin-squeezed states and NOON states (namely, the many-body version of Bell pairs). How can these states be produced? Are there situations where nature spontaneously forms them? Can we find thermal states which are resources for interferometry? In this work, we show that, in the vicinity of critical phase transitions, such interesting state do form spontaneously. They are, by definition, stable, being stabilized by thermal noise. We focus on the critical regime of the Ising model in a transverse field, in $d=1, 2, 3$, and infinite dimension (namely with infinite-range interactions). In large dimensions, the system is spin-squeezed, with a squeezing parameter saturating the quantum Fisher information (QFI). In other words: 1) the collective spin is able to probe rotations beyond the standard quantum limit; and 2) the optimal way to do so is to take advantage of the spin-squeezing. In low dimensions, the QFI diverges violently, almost saturating the Heisenberg limit. The spin-squeezing cannot explain this behavior, which is rather understood as a consequence of the proximity with a Schrödinger-cat NOON state. By construction, these states are stable to small perturbations, and we propose that they could be prepared quasi-adiabatically starting from a fully-polarized state.

Entanglement and entropy are key concepts standing at the foundations of quantum and statistical mechanics. In the last decade the study of quantum quenches revealed that these two concepts are intricately intertwined. Although the unitary time evolution ensuing from a pure initial state maintains the system globally at zero entropy, at long time after the quench local properties are captured by an appropriate statistical ensemble with non zero thermodynamic entropy, which can be interpreted as the entanglement accumulated during the dynamics. Therefore, understanding the post-quench entanglement evolution unveils how thermodynamics emerges in isolated quantum systems. An exact computation of the entanglement dynamics has been provided only for non-interacting systems, and it was believed to be unfeasible for genuinely interacting models. In this talk I show that the standard quasiparticle picture of the entanglement evolution, complemented with integrability-based knowledge of the asymptotic state, leads to a complete analytical understanding of the entanglement dynamics in the space-time scaling limit

Quantum information processing with trapped ions has a long and successful history. These techniques can be exploited for sensing application by forming "designer atoms" - quantum sensors which are based on multiple correlated atoms. Furthermore, characterizing the interactions that are the foundation for manipulating the quantum information is a crucial ingredient for building a quantum computers. These techniques can be directly used for quantum sensing applications in complex systems.

The Pauli exclusion principle forbids identical fermions from interacting via s-wave collisions. However, in the presence of spin-orbit coupling, identical fermions can experience effective interactions which can give rise to exotic topological and pairing behaviors, many of which have yet to be observed in condensed matter systems. Spin-orbit coupled alkaline-earth gases offer a promising pathway for quantum simulation of SOC physics given their long-lived electronic clock states which significantly reduce spontaneous emission and heating, as has been demonstrated in recent experiment. However, these first experiments were carried out in the dilute regime where single-particle physics dominates. Here I will report recent progress in one dimensional optical lattice clocks to enter the regime where interactions compete with single-particle effects. We perform time-resolved and controlled measurements of collective many-body dynamics after a sudden quench in a nuclear spin polarized 87Sr gas with an effective spin degree of freedom encoded in the clock states. Using Ramsey spectroscopy we observe a precession of the collective magnetization and signatures of spin locking effects arising from an interplay between p-wave and SOC induced s-wave interactions. The spin dynamics are well captured by a collective XXZ spin model that describes a broad class of condensed matter systems ranging from superconductors to quantum magnets.

Sensors based on single spins can enable magnetic field detection with very high sensitivity and spatial resolution. The key challenge in sensing is to achieve minimum estimation uncertainty within a given time and with a high dynamic range. Adaptive strategies have been proposed to achieve optimal performance but their implementation in solid-state systems has been hindered by the demanding experimental requirements. Here, I will report on our recent demonstration of adaptive sensing of a constant field, using a single electronic spin in a nitrogen-vacancy center in diamond. By adapting the spin readout basis in real time based on previous outcomes we report a sensitivity in Ramsey interferometry surpassing the standard measurement limit. By numerical simulations and experiments, we find that adaptive protocols offer a distinctive advantage over the best-known non-adaptive protocols when overhead and limited estimation time are taken into account. Additionally, I will discuss an adaptive protocol, based on Bayesian estimation, to a track a field with non-periodic variation described by a Wiener process. The tracking protocol updates the probability distribution for the magnetic field, based on measurement outcomes, and adapts the choice of sensing time and phase in real time. By taking the statistical properties of the signal into account, our protocol strongly reduces the required measurement time, reducing the error in the estimation of a time-varying signal by up to a factor 4.

Topological order is now being established as a central criterion for characterizing and classifying ground states of condensed matter systems and complements categorizations based on symmetries. Fractional quantum Hall systems and quantum spin liquids are receiving substantial interest because of their intriguing quantum correlations, their exotic excitations and prospects for protecting stored quantum information against errors. In this talk I will discuss our recent approach for implementing the Hamiltonian of the central model of this class of systems, the Toric Code, in lattices of superconducting circuits. The four-body interactions, which lie at its heart, are in our concept realised via Superconducting Quantum Interference Devices (SQUIDs) driven by a suitably oscillating flux bias. All physical qubits can be individually controlled and strings of operators acting on them, including the stabilizers, can be read out via a capacitive coupling to common transmission line resonators. The architecture we propose thus provides a versatile quantum simulator for topological order and lattice gauge theories. M. Sameti, A Potocnik, D. E. Browne, A. Wallraff, and M. J. Hartmann, Phys. Rev. A 95, 042330 (2017)

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 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. Finally, I will discuss how such strongly interacting, driven many-body systems can be harnessed for quantum enhanced metrology.

We experimentally investigate the tunneling dynamics between two 1D quasi Bose-Einstein condensates (1D-BEC) of 87Rb, magnetically trapped on an atom chip. The presence of interatomic interaction in our system makes its dynamics of strong interest as it allows the generation of number-squeezed states [1] and presents a relaxation through a mechanism still to be determined. The realization of number-squeezed states is presented in a first part of the talk. Starting with a single 1D-BEC, we perform an adiabatic deformation of the trap by radio-frequency dressing and obtain two 1D-BEC by splitting of the wave function. We demonstrated that interatomic interaction and tunneling during the splitting reduce the fluctuation of the atom number difference by 60% compared to a coherent state. The reduced number fluctuations and the very high coherence in our system lead to a -8 dB of spin squeezing, corresponding to the entanglement of about 10% of our atoms. In a second part of the talk, we make use of the possibility to imprint a global relative phase between the superfluids to investigate the tunneling dynamics for various coupling strengths. The observed dynamics exhibits a rapid relaxation toward a phase-locked equilibrium state, which goes beyond the 3D predictions of the two site Bose-Hubbard model. We currently include this relaxation as an empirical friction to investigate the dependence of the damping magnitude with our experimental parameters. It results that the relaxation does not depend on the tunnel coupling and depends on the atom number as N-1/2. We currently search for a relaxation mechanism compatible with our experimental observations. As the relaxation occurs with a time scale comparable with the splitting time presented in the first part of this talk, we expect that it plays a role in the generation of number-squeezing. [1] T. Berrada, S. van Frank, R. Bücker, T. Schumm, J.F. Schaff & J. Schmiedmayer, Integrated Mach-Zehnder interferometer for Bose-Einstein condensates, Nature Communications, 4, 2077 (2013).

I will give two examples of quantum sensing using correlated states, albeit few-body ones. The first example is how the formation of NOON states with spatially separated components is enabled through quantum walks of ultra-cold atoms in an optical lattice. The second example is that of an optomechanical system, where an entangled state of light and matter generated through the canonical trilinear radiation pressure interaction can be useful for gravitational accelerometry surpassing most of the current alternatives. Lastly, I will speak about a different topic -- how quantum entanglement inherent in a many-body mixed state, as quantified by the negativity, can be measured experimentally with a few copies of the state and machine learning methods.

Solid-state spins in diamond are a leading platform for quantum sensing under ambient conditions. Here I will present an approach to sensing that exploits controlled cross-relaxation between the sample and the probe spins, enabling all-optical spectroscopy of nearby electronic and nuclear spins, as well as hyperpolarisation of the sample's spins. I will also present recent applications of wide-field imaging using array of diamond spins, from biomagnetism to charge transport in graphene.

Quantum mechanics dictates that a continuous measurement of the position of an object imposes a random quantum back action (QBA) perturbation on its momentum. This randomness translates with time into position uncertainty, thus leading to the well known uncertainty on the measurement of motion. As a consequence, and in accordance with the Heisenberg uncertainty principle, the QBA puts a limitation—the so-called standard quantum limit—on the precision of sensing of position, velocity and acceleration. In this talk I will present the results of the experiment [1] where motion of a mechanical oscillator is tracked with the precision not restricted by the QBA. This is achieved by measuring the motion in a special reference frame linked to a system with an effective negative mass. Applications to sensing of forces and gravitational waves will be outlined. [1] Møller et al. arXiv:1856985 [quant-ph], to appear in Nature.

The Fisher information quantifies the sensitivity of a quantum state with respect to changes of a parameter. There exist bounds for the Fisher information of separable states and in order to achieve the largest possible sensitivities, entanglement between particles is needed. In this talk we derive general separability bounds that apply to discrete and continuous variable systems. We discuss applications to precision measurements and the characterization of topological quantum phase transitions.

Quantum metrology aims to yield higher measurement precisions via quantum techniques such as entanglement. It is of great importance for both fundamental sciences and practical technologies, from testing equivalence principle to designing high-precision atomic clocks. However, due to environment effects, highly entangled states become fragile and the achieved precisions may even be worse than the standard quantum limit (SQL). Here we present a high-precision measurement scheme via spin cat states (a kind of non-Gaussian entangled states in superposition of two quasi-orthogonal spin coherent states) under dissipation. In comparison to maximally entangled states, spin cat states with modest entanglement are more robust against losses and their achievable precisions may still beat the SQL. Even if the detector is imperfect, the achieved precisions of the parity measurement are higher than the ones of the population measurement. Our scheme provides a realizable way to achieve high-precision measurements via dissipative quantum systems of Bose atoms.

How much entanglement can be present in the ground state of simple local Hamiltonians? Surprisingly - quite a lot. In this talk, I will describe a continuous family of frustration-free Hamiltonians with exactly solvable ground states. The ground state of our model is non-degenerate and exhibits a novel quantum phase transition from a gapped phase with bounded entanglement entropy to a critical phase with a massively entangled state with volume entropy scaling. The ground state has simple geometrical interpretation in terms of colored Motzkin paths. I will also show an exact 'holographic' description of the state in terms of a tensor networks.

The theory of phase transitions plays a central role for the understanding of equilibrium physical systems. In this talk I will introduce a dynamical analogue, termed dynamical quantum phase transitions, occuring during nonequilibium quantum real-time evolution. I will summarize both the achieved advances, including the first experimental observations, and I will summarize how the dynamics of quantum entanglement is controlled by dynamical quantum phase transitions.

The accuracy of measurements is limited by quantum mechanics. Ingenious demonstrations, like measuring gravitational fields or time have explored accuracy limits and reached fundamental obstructions. Yet, precision measurements so far are restricted to macroscale and dedicated environments. In the talk I will discuss spin quantum sensors comprising a single electron spin plus a nuclear spin quantum register. With such a system we measure a variety of quantities including electric and magnetic fields, temperature, and force. We use nuclear spins to enhance the measurement accuracy of the electron spin e.g. via quantum error correction or as ancillary quantum bits as memory or for quantum Fourier transformation [1-3]. I will present a variety of applications ranging from quantum simulations to imaging of cellular structures. References [1] N. Aslam et al. Science 0.1126/science.aam8697 (2017) [2] L. Schlipf et al. Science Advances 3:e1701116 (2017) DOI: 10.1126/sciadv.1701116 [3] F. F. de Oliveira, et al. Nat. Commun. 8, 15409 doi: 10.1038/ncomms15409 (2017)

The phenomenon of quantum jumps between two states of a system submitted to continuous monitoring while being driven by a deterministic force is often exploited in precision quantum measurements. Quantum jumps are also emblematic of the special nature of randomness in quantum mechanics. In particular, the instants at which the jumps occur are reputed to be objectively random, and it has even been argued that their nature is fundamentally discontinuous. To the contrary, employing a 3-state artificial superconducting atom and a "super-QND" measurement of two of its levels, we experimentally show that, under the right conditions, it is possible to engineer a window of predictability in the dynamics of quantum jumps and witness their continuous character [1]. Our results are in agreement with quantum trajectory theory. The configuration employed in our experiment could be useful for the measurement of an error syndrome in quantum error correction. [1] Z. Minev, S.O. Mundhada, S. Shankar, P. Reinhold, L. Frunzio, R.J. Schoelkopf, M. Mirrahimi, H. Carmichael, M.H. Devoret (2017)

We show the emergence of topological Bogoliubov excitation in the strong coupling limit of a dimer chain realized with Josephson circuits. The appearance of midgap edge states can be detected in a reflection measurement. We propose a method to observe the winding of the topological phase across the Brillouin zone by scanning the phase of a time dependent modulation applied to the system.