Fast quantum interference of a nanoparticle via optical potential control.

We introduce and theoretically analyze a scheme to prepare and detect non-Gaussian quantum states of an optically levitated particle via the interaction with light pulses that generate cubic and inverted potentials. We show that this approach allows to operate on sufficiently short time- and length scales to beat decoherence in a regime accessible in state-of-the-art experiments. Specifically, we predict the observation of single-particle interference of a nanoparticle with a mass above 108 atomic mass units delocalized by several nanometers, on timescales of milliseconds. The proposed experiment uses only optical and electrostatic control, and can be performed at about 10-10 mbar and at room temperature. We discuss the prospect of this method for coherently splitting the wavepacket of massive dielectric objects without using either projective measurements or an internal level structure.

Tunable light-induced dipole-dipole interaction between optically levitated nanoparticles.

Arrays of optically trapped nanoparticles have emerged as a platform for the study of complex nonequilibrium phenomena. Analogous to atomic many-body systems, one of the crucial ingredients is the ability to precisely control the interactions between particles. However, the optical interactions studied thus far only provide conservative optical binding forces of limited tunability. In this work, we exploit the phase coherence between the optical fields that drive the light-induced dipole-dipole interaction to couple two nanoparticles. In addition, we effectively switch off the optical interaction and observe electrostatic coupling between charged particles. Our results provide a route to developing fully programmable many-body systems of interacting nanoparticles with tunable nonreciprocal interactions, which are instrumental for exploring entanglement and topological phases in arrays of levitated nanoparticles.

Non-Markovian Feedback Control and Acausality: An Experimental Study.

Causality is an important assumption underlying nonequilibrium generalizations of the second law of thermodynamics known as fluctuation relations. We here experimentally study the nonequilibrium statistical properties of the work and of the entropy production for an optically trapped, underdamped nanoparticle continuously subjected to a time-delayed feedback control. Whereas the non-Markovian feedback depends on the past position of the particle for a forward trajectory, it depends on its future position for a time-reversed path, and is therefore acausal. In the steady-state regime, we show that the corresponding fluctuation relations in the long-time limit exhibit a clear signature of this acausality, even though the time-reversed dynamics is not physically realizable.

Nonequilibrium Control of Thermal and Mechanical Changes in a Levitated System.

Fluctuation theorems are fundamental extensions of the second law of thermodynamics for small nonequilibrium systems. While work and heat are equally important forms of energy exchange, fluctuation relations have not been experimentally assessed for the generic situation of simultaneous mechanical and thermal changes. Thermal driving is indeed generally slow and more difficult to realize than mechanical driving. Here, we use feedback cooling techniques to implement fast and controlled temperature variations of an underdamped levitated microparticle that are 1 order of magnitude faster than the equilibration time. Combining mechanical and thermal control, we verify the validity of a fluctuation theorem that accounts for both contributions, well beyond the range of linear response theory. Our results allow the investigation of general far-from-equilibrium processes in microscopic systems that involve fast mechanical and thermal changes at the same time.

Real-time optimal quantum control of mechanical motion at room temperature.

The ability to accurately control the dynamics of physical systems by measurement and feedback is a pillar of modern engineering1. Today, the increasing demand for applied quantum technologies requires adaptation of this level of control to individual quantum systems2,3. Achieving this in an optimal way is a challenging task that relies on both quantum-limited measurements and specifically tailored algorithms for state estimation and feedback4. Successful implementations thus far include experiments on the level of optical and atomic systems5-7. Here we demonstrate real-time optimal control of the quantum trajectory8 of an optically trapped nanoparticle. We combine confocal position sensing close to the Heisenberg limit with optimal state estimation via Kalman filtering to track the particle motion in phase space in real time with a position uncertainty of 1.3 times the zero-point fluctuation. Optimal feedback allows us to stabilize the quantum harmonic oscillator to a mean occupation of 0.56 ± 0.02 quanta, realizing quantum ground-state cooling from room temperature. Our work establishes quantum Kalman filtering as a method to achieve quantum control of mechanical motion, with potential implications for sensing on all scales. In combination with levitation, this paves the way to full-scale control over the wavepacket dynamics of solid-state macroscopic quantum objects in linear and nonlinear systems.

Thermodynamics of continuous non-Markovian feedback control.

Feedback control mechanisms are ubiquitous in science and technology, and play an essential role in regulating physical, biological and engineering systems. The standard second law of thermodynamics does not hold in the presence of measurement and feedback. Most studies so far have extended the second law for discrete, Markovian feedback protocols; however, non-Markovian feedback is omnipresent in processes where the control signal is applied with a non-negligible delay. Here, we experimentally investigate the thermodynamics of continuous, time-delayed feedback control using the motion of an optically levitated, underdamped microparticle. We test the validity of a generalized second law which bounds the energy extracted from the system, and study the breakdown of feedback cooling for very large time delays.

Cooling of a levitated nanoparticle to the motional quantum ground state.

Quantum control of complex objects in the regime of large size and mass provides opportunities for sensing applications and tests of fundamental physics. The realization of such extreme quantum states of matter remains a major challenge. We demonstrate a quantum interface that combines optical trapping of solids with cavity-mediated light-matter interaction. Precise control over the frequency and position of the trap laser with respect to the optical cavity allowed us to laser-cool an optically trapped nanoparticle into its quantum ground state of motion from room temperature. The particle comprises 108 atoms, similar to current Bose-Einstein condensates, with the density of a solid object. Our cooling technique, in combination with optical trap manipulation, may enable otherwise unachievable superposition states involving large masses.

Cavity Cooling of a Levitated Nanosphere by Coherent Scattering.

We report three-dimensional (3D) cooling of a levitated nanoparticle inside an optical cavity. The cooling mechanism is provided by cavity-enhanced coherent scattering off an optical tweezer. The observed 3D dynamics and cooling rates are as theoretically expected from the presence of both linear and quadratic terms in the interaction between the particle motion and the cavity field. By achieving nanometer-level control over the particle location we optimize the position-dependent coupling and demonstrate axial cooling by two orders of magnitude at background pressures of 6×10^{-2} mbar. We also estimate a significant (>40 dB) suppression of laser phase noise heating, which is a specific feature of the coherent scattering scheme. The observed performance implies that quantum ground state cavity cooling of levitated nanoparticles can be achieved for background pressures below 1×10^{-7} mbar.

All-optical nanomechanical heat engine.

We propose and theoretically investigate a nanomechanical heat engine. We show how a levitated nanoparticle in an optical trap inside a cavity can be used to realize a Stirling cycle in the underdamped regime. The all-optical approach enables fast and flexible control of all thermodynamical parameters and the efficient optimization of the performance of the engine. We develop a systematic optimization procedure to determine optimal driving protocols. Further, we perform numerical simulations with realistic parameters and evaluate the maximum power and the corresponding efficiency.

Cavity cooling of an optically levitated submicron particle.

The coupling of a levitated submicron particle and an optical cavity field promises access to a unique parameter regime both for macroscopic quantum experiments and for high-precision force sensing. We report a demonstration of such controlled interactions by cavity cooling the center-of-mass motion of an optically trapped submicron particle. This paves the way for a light-matter interface that can enable room-temperature quantum experiments with mesoscopic mechanical systems.

Experimental entanglement of a six-photon symmetric Dicke state.

We report on the experimental observation and characterization of a six-photon entangled Dicke state. We obtain a fidelity as high as 0.654+/-0.024 and prove genuine six-photon entanglement by, amongst others, a two-setting witness yielding -0.422+/-0.148. This state has remarkable properties; e.g., it allows obtaining inequivalent entangled states of a lower qubit number via projective measurements, and it possesses a high entanglement persistency against qubit loss. We characterize the properties of the six-photon Dicke state experimentally by detecting and analyzing the entanglement of a variety of multipartite entangled states.

Experimental observation of an entire family of four-photon entangled states.

A single linear-optical setup is used to observe an entire family of four-photon entangled states. This approach breaks with the inflexibility of present linear-optical setups usually designed for the observation of a particular multipartite entangled state only. The family includes several prominent entangled states that are known to be highly relevant for quantum information applications.

Discriminating multipartite entangled states.

The variety of multipartite entangled states enables numerous applications in novel quantum information tasks. In order to compare the suitability of different states from a theoretical point of view, classifications have been introduced. Accordingly, here we derive criteria and demonstrate how to experimentally discriminate an observed state against the ones of certain other classes of multipartite entangled states. Our method, originating in Bell inequalities, adds an important tool for the characterization of multiparty entanglement.

Experimental direct observation of mixed state entanglement.

We report on the direct estimation of concurrence for mixed quantum states. The used method relies on joint measurements on two copies of an entangled state. In the experimental demonstration two polarization-entangled photon pairs emitted from spontaneous parametric down-conversion are analyzed together using a linear optics controlled phase gate. We demonstrate that the measured data, without need for further numerical processing, directly yield reliable estimates, despite experimental imperfections.

Entanglement persistency of multiphoton entangled states.

We experimentally demonstrate the entanglement persistency when losing photons in three- and four-photon polarization-entangled states. The entanglement properties of the mixed states obtained from multiphoton spontaneous parametric down-conversion are studied via witness and positive partial transpose approaches. Together with a quantification of the bipartite entanglement such analysis enables intuitive understanding of novel multiparty quantum communication protocols.

Experimental analysis of a four-qubit photon cluster state.

Linear-optics quantum logic operations enabled the observation of a four-photon cluster state. We prove genuine four-partite entanglement and study its persistency, demonstrating remarkable differences from the usual Greenberger-Horne-Zeilinger (GHZ) state. Efficient analysis tools are introduced in the experiment, which will be of great importance in further studies on multiparticle entangled states.

Linear optics controlled-phase gate made simple.

Linear optics quantum logic gates are the best tool to generate multiphoton entanglement. Simplifying a recent approach, we were able to implement the conditional phase gate with only one second-order interference at a polarization dependent beam splitter, thereby significantly increasing its stability. The improved quality of the gate is evaluated by analyzing its entangling capability and by performing full process tomography. The achieved results ensure that this device is well suited for implementation in various multiphoton quantum information protocols.

Experimental realization of a three-qubit entangled W state.

We report on the experimental observation of the three-photon polarization-entangled W state using spontaneous parametric down-conversion. This state is inequivalent to the Greenberger-Horne-Zeilinger state under stochastic local operations and classical communications and thus is the representative of the second class of genuine tripartite entanglement. We study the characteristic features of entanglement and demonstrate the high degree of two-photon entanglement in the W state.