Entropy production quantifies the amount of irreversibility of a physical process, leading to fundamental bounds for thermodynamic quantities. Particularly in the quantum realm, considerable research has been carried out in the last decades extending entropy production to nonequilibrium processes. We experimentally investigate the entropy production of forward-backward cycles containing different decorrelating processes realized to erase different types of correlations between two interacting systems, from obliterating solely quantum coherence to completely decorrelating local states. We apply these processes to the entanglement of a two-level atom, realized with a circular Rydberg atom, and a light field of a high-quality microwave cavity. The entropy production is computed from the full quantum-state tomography of the system performed at different stages of the interaction-decorrelation sequence. Due to the quantum nature of the atom-cavity system, we find that, although standard, the maximum likelihood estimation method for the density matrix leads to spurious divergences of the entropy production. We propose and implement an alternative estimator that remedies such divergences. Our work experimentally assesses irreversibility of non-thermal processes and addresses the care that must be taken in handling experimental data to estimate the entropy production.

We study in detail the mechanisms causing dephasing of hyperfine coherences of cesium atoms confined by a far off-resonant standing wave optical dipole trap [S. Kuhr et al., Phys. Rev. Lett. 91, 213002 (2003)]. Using Ramsey spectroscopy and spin echo techniques, we measure the reversible and irreversible dephasing times of the ground state coherences. We present an analytical model to interpret the experimental data and identify the homogeneous and inhomogeneous dephasing mechanisms. Our scheme to prepare and detect the atomic hyperfine state is applied at the level of a single atom as well as for ensembles of up to 50 atoms.

We theoretically derive and experimentally compare several different ways to access entropy production in a quantum process under feedback control. We focus on a bipartite quantum system realizing an autonomous Maxwell's demon scheme reported by Najera-Santos et al. [Phys.~Rev.~Research 2, 032025(R) (2020)], where information encoded in a demon is consumed to transfer heat from a cold qubit to a hot cavity. By measuring individual quantum trajectories of the joint demon-cavity-qubit system, we compute the entropy production with six distinct expressions derived from different approaches to the system description and its evolution. Each method uses a specific set of trajectories and data processing. Our results provide a unified view on the various meanings of irreversibility in quantum systems and pave the way to the measurement of entropy production beyond thermal frameworks.

We theoretically derive and experimentally compare six different ways to access entropy production in a cavity QED process. We focus on a bipartite quantum system under feedback control realizing an autonomous Maxwell's demon scheme reported by Najera-Santos et al. [Phys. Rev. Research 2, 032025(R) (2020)], where information encoded in a demon is consumed to transfer heat from a cold qubit to a hot cavity. By measuring individual quantum trajectories of the joint demon-cavity-qubit system, we compute the entropy production with six suggested expressions each using a specific set of trajectories and a specific data processing. These expressions show different sensitivity to experimental imperfections as revealed by numerical simulations, allowing to adapt a particular measurement strategy to specific experimental limitations. Our results provide a unified view on the various meanings of irreversibility in quantum systems. They pave the way to the measurement of entropy production beyond thermal frameworks.

We present an autonomous Maxwell's demon scheme. It is first analysed theoretically in term of information exchange in a closed system and then implemented experimentally with a single Rydberg atom and a high-quality microwave resonator. The atom simulates both a qubit interacting with the cavity, and a demon carrying information on the qubit state. While the cold qubit crosses the hot cavity, the demon prevents energy absorption from the cavity mode, apparently violating the second law of thermodynamics. Taking into account the change of the mutual information between the demon and the qubit-cavity system gives rise to a generalized expression of the second law that we establish and measure. Finally, considering the closed qubit-cavity-demon system, we establish and measure that the generalized second law can be recast into an entropy conservation law, as expected for a unitary evolution.

The simple resonant Rabi oscillation of a two-level system in a single-mode coherent field reveals complex features at the mesoscopic scale, with oscillation collapses and revivals. Using slow circular Rydberg atoms interacting with a superconducting microwave cavity, we explore this phenomenon in an unprecedented range of interaction times and photon numbers. We demonstrate the efficient production of cat states, which are the quantum superposition of coherent components with nearly opposite phases and sizes in the range of few tens of photons. We measure cuts of their Wigner functions revealing their quantum coherence and observe their fast decoherence. This experiment opens promising perspectives for the rapid generation and manipulation of nonclassical states in cavity and circuit quantum electrodynamics.

The efficient quantum state reconstruction algorithm described by Six et al. [Phys. Rev. A 93, 012109 (2016)PLRAAN2469-992610.1103/PhysRevA.93.012109] is experimentally implemented on the nonlocal state of two microwave cavities entangled by a circular Rydberg atom. We use information provided by long sequences of measurements performed by resonant and dispersive probe atoms over timescales involving the system decoherence. Moreover, we benefit from the consolidation, in the same reconstruction, of different measurement protocols providing complementary information. Finally, we obtain realistic error bars for the matrix elements of the reconstructed density operator. These results demonstrate the pertinence and precision of the method, directly applicable to any complex quantum system.

We propose an extension of the maximum-likelihood method applied to a set of quantum trajectories and their measurement records. Along with the reconstruction of the quantum state evolution, it allows to estimate unknown multi-dimensional parameter.

We report a quantum measurement beyond the standard quantum limit (SQL) for the amplitude of a small displacement acting on a cavity field. This measurement uses as a resource an entangled mesoscopic state, prepared by the resonant interaction of a circular Rydberg atom with a field stored in a superconducting cavity. We analyze the measurement process in terms of Fisher information and prove that it is, in principle, optimal. The experimental precision achieved, 2.4 dB below the SQL, is well understood in terms of experimental imperfections. This method could be transposed to other systems, particularly to circuit QED, for the precise measurement of weak forces acting on oscillators.

Tomography of a quantum state is usually based on a positive-operator-valued measure (POVM) and on their experimental statistics. Among the available reconstructions, the maximum-likelihood (MaxLike) technique is an efficient one. We propose an extension of this technique when the measurement process cannot be simply described by an instantaneous POVM. Instead, the tomography relies on a set of quantum trajectories and their measurement records. This model includes the fact that, in practice, each measurement could be corrupted by imperfections and decoherence, and could also be associated with the record of continuous-time signals over a finite amount of time. The goal is then to retrieve the quantum state that was present at the start of this measurement process. The proposed extension relies on an explicit expression of the likelihood function via the effective matrices appearing in quantum smoothing and solutions of the adjoint quantum filter. It allows us to retrieve the initial quantum state as in standard MaxLike tomography, but where the traditional POVM operators are replaced by more general ones that depend on the measurement record of each trajectory. It also provides, aside from the MaxLike estimate of the quantum state, confidence intervals for any observable. Such confidence intervals are derived, as the MaxLike estimate, from an asymptotic expansion of multidimensional Laplace integrals appearing in Bayesian mean estimation. A validation is performed on two sets of experimental data: photon(s) trapped in a microwave cavity subject to quantum nondemolition measurements relying on Rydberg atoms, and heterodyne fluorescence measurements of a superconducting qubit.

A quantum system can be monitored through repeated interactions with meter systems. The state of the system at time t, represented by the density matrix rho(t), then becomes conditioned on the information obtained by the meters until that time. More insight in the state of the system at any time t is provided, however, by taking into account the full detection of all meters interacting with the system both in the past and in the future of t. We present experiments that use near-resonant atomic probes to monitor the evolution of the quantized field in a cavity. The application of the forward-backward smoothing method to this quantum problem, justified by the past quantum state formalism [S. Gammelmark et al., Phys. Rev. Lett. 111, 160401 (2013)], allows us to resolve a posteriori dynamics, which is not reflected by the usual quantum state rho(t).

We measure the photon number in a microwave cavity probed by circular Rydberg atoms using the Past Quantum State approach. It leads to a considerable noise reduction and allows us to access normally hidden information.

The estimation of the state of a quantum system is a central task in quantum information and quantum-enabled metrology. A quantum system can be monitored indirectly through its successive interaction with meters, whose final detection provides information on the system’s state. In the standard, forward, approach, the system’s density operator, ρ, at time t is deduced from all measurements performed up to time t and from our knowledge of the system’s dynamics, including relaxation. The recently introduced past quantum state (PQS) formalism [1] provides us with a simple method to include in the state estimation also information gathered after t. We present here an experiment applying the PQS analysis to a system with a high-dimensional Hilbert space [2].

The back-action of a quantum measurement with a degenerate eigenvalue confines the evolution of the system inside the corresponding eigenspace. Using the Stark sublevels of a Rydberg atom, we report the first observation of such quantum Zeno dynamics in a non-trivial 51-dimension Hilbert space.

A quantum system can be monitored through repeated interactions with meters, followed by their detection. The state of the system at time t is thus conditioned on the information obtained until that time. More insight in the state dynamics is provided, however, by the past quantum state (PQS) [S. Gammelmark et al. Phys. Rev. Lett. 111, 160401 (2013)]. It relies on all aspects of the system evolution which are recorded in the past and in the future of t. Using PQS analysis for the quantum non-demolition photon number counting in a cavity, we can reveal information hidden in the standard approach and resolve a wider range of number states. This experiment demonstrates the strong potential of PQS analysis.

The efficient initialization of a quantum system is a prerequisite for quantum technological applications. Here we show that several classes of quantum states of a harmonic oscillator can be efficiently prepared by means of a Jaynes-Cummings interaction with a single two-level system. This is achieved by suitably tailoring external fields which drive the dipole and/or the oscillator. The time-dependent dynamics that leads to the target state is identified by means of optimal control theory (OCT) based on Krotov's method. Infidelities below ${10}^{\ensuremath{-}4}$ can be reached for the parameters of the experiment of Raimond, Haroche, Brune and co-workers, where the oscillator is a mode of a high-Q microwave cavity and the dipole is a Rydberg transition of an atom. For this specific situation we analyze the limitations on the fidelity due to parameter fluctuations and identify robust dynamics based on pulses found using ensemble OCT. Our analysis can be extended to quantum-state preparation of continuous-variable systems in other platforms, such as trapped ions and circuit QED.

Superconducting atom chips and Rydberg atoms are promising tools for quantum information processing operations based on the dipole blockade effect. Nevertheless, one has to face the severe problem of stray electric fields in the vicinity of the chip. We demonstrate a simple method circumventing this problem. Microwave spectroscopy reveals extremely long coherence lifetimes (in the millisecond range) for a qubit stored in a Rydberg level superposition close to the chip surface. This is an essential step for the development of quantum simulations with Rydberg atoms and of a hybrid quantum information architecture based on atomic ensembles and superconducting circuits.

In a quantum world, a watched arrow never moves. This is the Quantum Zeno Effect (QZE). Repeatedly asking a quantum system "are you still in your initial state?" blocks its coherent evolution through measurement back-action. Quantum Zeno Dynamics (QZD) leaves more freedom to the system. Instead of pinning it to a single state, it sets a border in its evolution space. Repeatedly asking the system "did you cross the border?" makes it impenetrable. Since the border can be designed at will by choosing the measured observable, QZD allows one to tailor the system's evolution space. Recent proposals, particularly in the Cavity Quantum Electrodynamics (CQED) context, highlight the interest of QZD for quantum state engineering tasks, which are the key to quantumenabled technologies and quantum information processing. We report the observation of QZD in the 51-dimension Hilbert space of a large angular momentum J = 25. Continuous selective interrogation limits the evolution of this angular momentum to an adjustable multi-dimensional subspace. This confined dynamics leads to the production of non-classical "Schrödinger cat" states, quantum superpositions of angular momentums pointing in different directions. These states are promising for sensitive metrology of electric and magnetic fields. This QZD approach could be generalized to other systems, opening novel perspectives for quantum information processing.

Because of their very large polarizability, Rydberg atoms have long-range interaction through dipole-dipole coupling. Rydberg excitations in a cold atomic sample are therefore expected to exhibit many-body correlations and could be used to simulate many-body Hamiltonians to understand complex and less controllable solid-states system [1, 2]. Our experiment uses a superconducting atom chip to trap and manipulate a small Rb atom cloud in a cryogenic environment. Manipulating Rydberg atoms close to a chip is very challenging, as the Rydberg atom polarizability makes them very sensitive to stray electric eld created by the surface. We had therefore to develop a new method to reduce the broadening of the Rydberg excitation line. By coating our chip with a thin layer of Rubidium, we have been able to strongly reduce electric eld inhomogeneity and observe coherence time on the 60s 61s transition in the ms range. Then, using a cold atom cloud near Bose-Einstein condensation, we have produced samples of tens of Rydberg and used microwave spectroscopy to measure the distribution of the interaction energy of a single Rydberg atom with its neighbors. We see that if the laser frequency is detuned from the transition frequency, we can preferably excite atoms close to each other, for which the dipole-dipole interaction compensate the laser detuning. We can then monitor the motion of the atoms, by recording the energy distribution for di erent delay after the excitation, and observe how the Rydberg atom sample explode under the e ect of the energy interaction.