Quantum Sensing with Quantum Correlated Systems

Photon-mediated interactions among atoms coupled to an optical cavity are a powerful tool for engineering quantum many-body Hamiltonians. We present an experiment aimed at generating non-local and dynamically controllable spin-spin interactions by strongly coupling 87Rb atoms to a near-concentric cavity. The tightly-focused waist of 11um combined with a high finesse of 60,000 yields a single-atom cooperativity of 50. Furthermore, the optical access afforded by the near-concentric geometry enables imaging and addressing with 1um resolution. We detail the current status of the experiment and progress toward many-body quantum control.

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.

The experimental interest in realizing quantum spin-1/2-chains has increased uninterruptedly over the last decade. In many instances, the target quantum simulation belongs to the broader class of non-interacting fermionic models, constituting an important benchmark. In spite of this class being analytically efficiently tractable, no direct certification tool has yet been reported for it. In fact, in experiments, certification has almost exclusively relied on notions of quantum state tomography scaling very unfavorably with the system size. Here, we develop experimentally-friendly fidelity witnesses for all pure fermionic Gaussian target states. Their expectation value yields a tight lower bound to the fidelity and can be measured efficiently. We derive witnesses in full generality in the Majorana-fermion representation and apply them to experimentally relevant spin-1/2 chains. Among others, we show how to efficiently certify strongly out-of-equilibrium dynamics in critical Ising chains. At the heart of the measurement scheme is a variant of importance sampling specially tailored to overlaps between covariance matrices. The method is shown to be robust against finite experimental-state infidelities.

In this work, we present a result on the non-equilibrium dynamics causing equilibration and Gaussification of quadratic non-interacting fermionic Hamiltonians. Specifically, based on two basic assumptions - clustering of correlations in the initial state and the Hamiltonian exhibiting delocalizing transport - we prove that non-Gaussian initial states become locally indistinguishable from fermionic Gaussian states after a short and well controlled time. This relaxation dynamics is governed by a power-law independent of the system size. Our argument is general enough to allow for pure and mixed initial states, including thermal and ground states of interacting Hamiltonians on and large classes of lattices as well as certain spin systems. The argument gives rise to rigorously proven instances of a convergence to a generalized Gibbs ensemble. Our results allow to develop an intuition of equilibration that is expected to be more generally valid and relates to current experiments of cold atoms in optical lattices.

Entangled states have the potential to enable metrology beyond the standard quantum limit (SQL). Spin-squeezed states [1], as one of the primary examples of highly entangled states, are particularly interesting for state-of-the-art atomic clocks and interferometers in which the SQL is an obstacle today. On the technological side, atom chips provide a robust, miniature platform which has been used to realize compact atomic clocks and as a fast source of BECs for atom interferometers [2]. In our Trapped Atom Clock on a Chip (TACC), we reached a stablility of 6E-13 at 1s [3]. Here we show that spin squeezing can be generated spontaneously in a rubidium BEC [4], without the need for Feshbach resonaces or state-dependent potentials [5]. Furthermore, in the new experiment, we target a quantum-enhanced version of the TACC atomic clock, using spin-squeezed ultra-cold thermal atoms generated by cavity-QED interactions [6,7]. To reach this goal, we have integrated two fiber Fabry-Perot cavities [8] on the clock chip, realizing a platform for cavity-QED in the strong coupling and weak coupling regime respectively. With this new device, we aim to explore spin squeezing at a metrologically relevant level of precision. [1] M. Kitagawa and M. Ueda, Phys. Rev. A, 47, 5138 (1993) [2] J. Reichel and V. Vuletić (ed.), Atom chips, Wiley (2011) [3] R. Szmuk, et al., Phys. Rev. A 92, 012106 (2015) [4] T. Laudat, et al., in preparation [5] M. Riedel, et al., Nature 464, 1170 (2010) [6] I. Leroux, et al., Phys. Rev. Lett. 104, 073602 (2010) [7] O. Hosten, et al., Nature 529, 505 (2016) [8] K. Ott, et al., Optics Express 24, 9839 (2016)

Spin-orbit coupling exists in materials in general. However, it entangles the spin and orbital degrees of freedom and complicates the model. Thus, theorists usually neglect the effects induced by spin-orbit coupling first and consider spin-orbit coupling as perturbation next. The non-perturbative effects brought up by spin-orbit coupling are thus often less studied or overlooked. On the other hand, the majority in the study of interacting topological order focusing on the mathematical structure of theories and made significant advances by leaving material details behind. It is thus important to find possible microscopic models that could realize the new phases in laboratories and benefits from the progress of theories to make experimental predictions. I will discuss the physical effects due to strong spin-orbit coupling from the perspective of searching new quantum orders and the non-trivial responses. We found a physical mechanism that realizes interesting models which can have non-trivial long range entangled phases in both 3D pyrochlore lattice and 2D Kagome lattice under different physical conditions. The 3D model can realize two distinct quantum spin ice phases, i.e. dipolar and octupolar quantum spin ices. The 2D model can realize a Z2 topological order with nontrivial symmetry fractionalization pattern. The particular Z2 topological order can be detected numerically or experimentally by the "vison zero modes" which is a remarkable topological signature induced by the onsite Ising symmetry and the space group symmetry. References: Yi-Ping Huang*, Gang Chen and Michael Hermele, PRL 112, 167203 (2014) Yi-Ping Huang* and Michael Hermele, PRB 95, 075130 (2017)

Three-dimensional frustrated magnets have recently come into limelight as promising candidates to host the much sought after quantum spin liquid phase. Recent experiments on pyrochlore, hyperkagome, and diamond lattice compounds have revealed the presence of tremendously interesting and intriguing low-energy physics. However, progress on the theoretical front is lacking due to a complete vacuum of numerical many-body methods which can address three-dimensional spin systems of large enough size enabling reliable conclusions in the thermodynamic limit. Using the recently developed pseudo-fermion functional renormalization group (PFFRG) method which efficiently handles 3D spin systems, we address the low-energy physics of different spin liquid candidate materials in 3D which have been the subject of recent experimental investigation. The spin susceptibility profiles obtained within PFFRG are shown to be in excellent agreement with available neutron scattering data, which displays fascinating features, such as the presence of cogwheels, boomerangs, and bow-ties.

Large ensembles of ultra-cold atoms offer the possibility to generate an unprecedented level of multi-particle entanglement. However, the creation relies on the fundamental indistinguishability of the particles. Most quantum information applications require the addressability and therefore the distinguishability of individual subsystems. Employing spin changing collisions, we generate entanglement between two spatially separated atomic clouds. We verify the entanglement between the clouds with a novel criterion, which accounts for imperfections of the state preparation, e.g. varying atom numbers in our condensate and the imperfect symmetry of the state.

We study a quantum dissipative phase model in which each local phase-difference and each local momentum are uniformly coupled to two different baths. Such a system can represent e.g. a chain of resistively shunted Josephson junctions [1], capacitively coupled to a diffusive metal [2]. The first dissipative coupling quenches the quantum phase fluctuations favoring the phase order whereas the second one quenches momentum fluctuations destroying phase coherence. Using the self-consistent harmonic approximation [1], we construct a zero-temperature phase diagram. As an effect of the quantum frustration for the two canonical conjugate observables [3,4], we obtain an interesting phase diagram with a non monotonic behavior. [1] S. Chakravarty et al., Phys. Rev. Lett. \textbf{56}, 2303 (1986). [2] A.M.Lobos, T. Giamarchi, Phys. Rev. B \textbf{84}, 024523 (2011). [3] H. Kohler, F. Sols, New J. Phys. \textbf{8}, 149 (2006). [4] & G. Rastelli, New J. Phys. \textbf{18}, 053033 (2016).

We consider the problem of estimating the temperature $T$ of a very cold equilibrium sample. To this end we have worked on two different scenarios: 1-Using the criticality of quantum many-body systems. Within this frame we examine the spin-1/2 XY chain, first estimating, by means of the quantum Fisher information, the lowest attainable bound on the temperature precision. We observe that, indeed, the criticality is a resource for low-$T$ metrology, even at finite temperatures. We then address the estimation of the temperature of the sample from the analysis of correlations using a quantum non demolishing Faraday spectroscopy method. Remarkably, our results show that the collective quantum correlations can become optimal observables to accurately estimate the temperature of our model in a given range of temperatures. 2-By establishing a strong coupling of the sample under study to the thermometer. The temperature estimates are drawn from measurements performed on a quantum probe srongly coupled to it. We model this scenario by resorting to the canonical Caldeira-Leggett Hamiltonian and find analytically the exact stationary state of the probe for arbitrary coupling strength. In general, the probe does not reach thermal equilibrium with the sample, due to their non-perturbative interaction. We argue that this is advantageous for low temperature thermometry, as we show in our model that: (i) The thermometric precision at low $T$ can be significantly enhanced by strengthening the probe-sampling coupling, (ii) the variance of a suitable quadrature of our Brownian thermometer can yield temperature estimates with nearly minimal statistical uncertainty, and (iii) the spectral density of the probe-sample coupling may be engineered to further improve thermometric performance. These observations may find applications in practical nanoscale thermometry at low temperatures---a regime which is particularly relevant to quantum technologies.

We studied conductance of a quantum dots (QD) from carbon nanotubes in dependence on different strength of Coulomb repulsion between leads and QD. In such QD electron state is determined by the spin quantum number and also with an extra spin orbital quantum number. Our computational approach took into account the spin-orbit interaction and the Coulomb repulsion both between electrons on a QD as well as between the QD electron and contacts. We utilized an approach developed by us earlier in [1,2], which is based on the Keldysh non-equilibrium Green’s function formalism as well as the equation of motion technique. We focused on the case of different strength of Coulomb repulsion between leads and QD and infinite Coulombic on-site repulsion and considered two possible cases of applied voltage: spin bias and conventional bias. Presence of the QD-lead interaction yields formation of a new pair of peaks in the differential conductance dependence. It was shown that increase of the QD-lead interaction leads to an overall shift of the density of electronic states dependence toward higher energy values. We also show that existence of four quantum states in a QD leads to abrupt changes in the density of states. Strong dependence on the parameters of Coulomb repulsion was observed. We predict that current could be substantially altered in the presence of, e.g., drug molecules for detecting which such nanotube-QD based sensor could be used.

A key resource for distributed quantum-enhanced protocols is entangled states between spatially separated modes. Here, we use spin mixing in a tightly confined Bose-Einstein condensate of 87Rb to generate a squeezed vacuum state in a single spatial mode. We show experimentally that the corresponding local entanglement can be spatially distributed by self-similar expansion of the atomic cloud in a waveguide potential. Spatially resolved spin read-out is used to reveal Einstein-Podolsky-Rosen (EPR) steering between distinct parts of the expanded cloud. Building on the ability to partition the system arbitrarily, we also show threeway steering. To quantify the connection between the strength of EPR steering and genuine multipartite entanglement we construct a witness, which testifies up to genuine five-partite entanglement.

First order quantum phase transitions (1QPTs) are signaled, in the thermodynamic limit, by discontinuous changes in the ground state properties. These discontinuities affect expectation values of observables, including spatial correlations. When a 1QPT is crossed in the vicinity of a second order one (2QPT), due to the correlation length divergence to the later, the corresponding ground state is modified and it becomes increasingly difficult to determine the order of the transition when the size of the system is finite. Here we show that, in such situations, it is possible to apply finite size scaling to entanglement measures, as it has recently been done for the order parameters and the energy gap in order to recover the correct thermodynamic limit. Such finite size scaling can unambigously discriminate between first and second order phase transitions in the vicinity of multricritical points even when the singularities displayed by entanglement measures lead to controversial results.