Nonreciprocal control and cooling of phonon modes in an optomechanical system.

Mechanical resonators are important components of devices that range from gravitational wave detectors to cellular telephones. They serve as high-performance transducers, sensors and filters by offering low dissipation, tunable coupling to diverse physical systems, and compatibility with a wide range of frequencies, materials and fabrication processes. Systems of mechanical resonators typically obey reciprocity, which ensures that the phonon transmission coefficient between any two resonators is independent of the direction of transmission1,2. Reciprocity must be broken to realize devices (such as isolators and circulators) that provide one-way propagation of acoustic energy between resonators. Such devices are crucial for protecting active elements, mitigating noise and operating full-duplex transceivers. Until now, nonreciprocal phononic devices3-11 have not simultaneously combined the features necessary for robust operation: strong nonreciprocity, in situ tunability, compact integration and continuous operation. Furthermore, they have been applied only to coherent signals (rather than fluctuations or noise), and have been realized exclusively in travelling-wave systems (rather than resonators). Here we describe a scheme that uses the standard cavity-optomechanical interaction to produce robust nonreciprocal coupling between phononic resonators. This scheme provides about 30 decibels of isolation in continuous operation and can be tuned in situ simply via the phases of the drive tones applied to the cavity. In addition, by directly monitoring the dynamics of the resonators we show that this nonreciprocity can control thermal fluctuations, and that this control represents a way to cool phononic resonators.

Stabilized entanglement of massive mechanical oscillators.

Quantum entanglement is a phenomenon whereby systems cannot be described independently of each other, even though they may be separated by an arbitrarily large distance 1 . Entanglement has a solid theoretical and experimental foundation and is the key resource behind many emerging quantum technologies, including quantum computation, cryptography and metrology. Entanglement has been demonstrated for microscopic-scale systems, such as those involving photons2-5, ions 6 and electron spins 7 , and more recently in microwave and electromechanical devices8-10. For macroscopic-scale objects8-14, however, it is very vulnerable to environmental disturbances, and the creation and verification of entanglement of the centre-of-mass motion of macroscopic-scale objects remains an outstanding goal. Here we report such an experimental demonstration, with the moving bodies being two massive micromechanical oscillators, each composed of about 10 12 atoms, coupled to a microwave-frequency electromagnetic cavity that is used to create and stabilize the entanglement of their centre-of-mass motion15-17. We infer the existence of entanglement in the steady state by combining measurements of correlated mechanical fluctuations with an analysis of the microwaves emitted from the cavity. Our work qualitatively extends the range of entangled physical systems and has implications for quantum information processing, precision measurements and tests of the limits of quantum mechanics.

Competition between Two-Photon Driving, Dissipation, and Interactions in Bosonic Lattice Models: An Exact Solution.

We present an exact solution in arbitrary dimensions for the steady states of a class of quantum driven-dissipative bosonic models, where a set of modes is subject to arbitrary two-photon driving, single-photon loss, and a global Hubbard (or Kerr)-like interaction. Our solutions reveal a wealth of striking phenomena, including the emergence of dissipative phase transitions, nontrivial mode competition physics and symmetry breaking, and the stabilization of many-body SU(1,1) pair-coherent states. Our exact solutions enable the description of spatial correlations, and are fully valid in regimes where traditional mean-field and semiclassical approaches break down.

Exact Solution of the Infinite-Range Dissipative Transverse-Field Ising Model.

The dissipative variant of the Ising model in a transverse field is one of the most important models in the analysis of open quantum many-body systems, due to its paradigmatic character for understanding driven-dissipative quantum phase transitions, as well as its relevance in modeling diverse experimental platforms in atomic physics and quantum simulation. Here, we present an exact solution for the steady state of the transverse-field Ising model in the limit of infinite-range interactions, with local dissipation and inhomogeneous transverse fields. Our solution holds despite the lack of any collective spin symmetry or even permutation symmetry. It allows us to investigate first- and second-order dissipative phase transitions, driven-dissipative criticality, and captures the emergence of a surprising "spin blockade" phenomenon. The ability of the solution to describe spatially varying local fields provides a new tool to study disordered open quantum systems in regimes that would be extremely difficult to treat with numerical methods.

Squeezed Superradiance Enables Robust Entanglement-Enhanced Metrology Even with Highly Imperfect Readout.

Quantum metrology protocols using entangled states of large spin ensembles attempt to achieve measurement sensitivities surpassing the standard quantum limit (SQL), but in many cases they are severely limited by even small amounts of technical noise associated with imperfect sensor readout. Amplification strategies based on time-reversed coherent spin-squeezing dynamics have been devised to mitigate this issue, but are unfortunately very sensitive to dissipation, requiring a large single-spin cooperativity to be effective. Here, we propose a new dissipative protocol that combines amplification and squeezed fluctuations. It enables the use of entangled spin states for sensing well beyond the SQL even in the presence of significant readout noise. Further, it has a strong resilience against undesired single-spin dissipation, requiring only a large collective cooperativity to be effective.

Dissipative Pairing Interactions: Quantum Instabilities, Topological Light, and Volume-Law Entanglement.

We analyze an unusual class of bosonic dynamical instabilities that arise from dissipative (or non-Hermitian) pairing interactions. We show that, surprisingly, a completely stable dissipative pairing interaction can be combined with simple hopping or beam-splitter interactions (also stable) to generate instabilities. Further, we find that the dissipative steady state in such a situation remains completely pure up until the instability threshold (in clear distinction from standard parametric instabilities). These pairing-induced instabilities also exhibit an extremely pronounced sensitivity to wave function localization. This provides a simple yet powerful method for selectively populating and entangling edge modes of photonic (or more general bosonic) lattices having a topological band structure. The underlying dissipative pairing interaction is experimentally resource friendly, requiring the addition of a single additional localized interaction to an existing lattice, and is compatible with a number of existing platforms, including superconducting circuits.

Single-Spin Readout and Quantum Sensing Using Optomechanically Induced Transparency.

Solid-state spin defects are promising quantum sensors for a large variety of sensing targets. Some of these defects couple appreciably to strain in the host material. We propose to use this strain coupling for mechanically mediated dispersive single-shot spin readout by an optomechanically induced transparency measurement. Surprisingly, the estimated measurement times for negatively charged silicon-vacancy defects in diamond are an order of magnitude shorter than those for single-shot optical fluorescence readout. Our scheme can also be used for general parameter-estimation metrology and offers a higher sensitivity than conventional schemes using continuous position detection.

Exact Solutions of Interacting Dissipative Systems via Weak Symmetries.

We demonstrate how the presence of continuous weak symmetry can be used to analytically diagonalize the Liouvillian of a class of Markovian dissipative systems with strong interactions or nonlinearity. This enables an exact description of the full dynamics and dissipative spectrum. Our method can be viewed as implementing an exact, sector-dependent mean-field decoupling, or alternatively, as a kind of quantum-to-classical mapping. We focus on two canonical examples: a nonlinear bosonic mode subject to incoherent loss and pumping, and an inhomogeneous quantum Ising model with arbitrary connectivity and local dissipation. In both cases, we calculate and analyze the full dissipation spectrum. Our method is applicable to a variety of other systems, and could provide a powerful new tool for the study of complex driven-dissipative quantum systems.

Heisenberg-Limited Spin Squeezing via Bosonic Parametric Driving.

Spin-spin interactions generated by a detuned cavity are a standard mechanism for generating highly entangled spin squeezed states. We show here how introducing a weak detuned parametric (two-photon) drive on the cavity provides a powerful means for controlling the form of the induced interactions. Without a drive, the induced interactions cannot generate Heisenberg-limited spin squeezing, but a weak optimized drive gives rise to an ideal two-axis twist interaction and Heisenberg-limited squeezing. Parametric driving is also advantageous in regimes limited by dissipation, and enables an alternate adiabatic scheme which can prepare optimally squeezed, Dicke-like states. Our scheme is compatible with a number of platforms, including solid-state systems where spin ensembles are coupled to superconducting quantum circuits or mechanical modes.

Initialization of Single Spin Dressed States using Shortcuts to Adiabaticity.

We demonstrate the use of shortcuts to adiabaticity protocols for initialization, read-out, and coherent control of dressed states generated by closed-contour, coherent driving of a single spin. Such dressed states have recently been shown to exhibit efficient coherence protection, beyond what their two-level counterparts can offer. Our state transfer protocols yield a transfer fidelity of ∼99.4(2)% while accelerating the transfer speed by a factor of 2.6 compared to the adiabatic approach. We show bidirectionality of the accelerated state transfer, which we employ for direct dressed state population read-out after coherent manipulation in the dressed state manifold. Our results enable direct and efficient access to coherence-protected dressed states of individual spins and thereby offer attractive avenues for applications in quantum information processing or quantum sensing.

Enhancing Cavity Quantum Electrodynamics via Antisqueezing: Synthetic Ultrastrong Coupling.

We present and analyze a method where parametric (two-photon) driving of a cavity is used to exponentially enhance the light-matter coupling in a generic cavity QED setup, with time-dependent control. Our method allows one to enhance weak-coupling systems, such that they enter the strong coupling regime (where the coupling exceeds dissipative rates) and even the ultrastrong coupling regime (where the coupling is comparable to the cavity frequency). As an example, we show how the scheme allows one to use a weak-coupling system to adiabatically prepare the highly entangled ground state of the ultrastrong coupling system. The resulting state could be used for remote entanglement applications.

Stroboscopic Qubit Measurement with Squeezed Illumination.

Microwave squeezing represents the ultimate sensitivity frontier for superconducting qubit measurement. However, measurement enhancement has remained elusive, in part because integration with standard dispersive readout pollutes the signal channel with antisqueezed noise. Here we induce a stroboscopic light-matter coupling with superior squeezing compatibility, and observe an increase in the final signal-to-noise ratio of 24%. Squeezing the orthogonal phase slows measurement-induced dephasing by a factor of 1.8. This scheme provides a means to the practical application of squeezing for qubit measurement.

Negative Full Counting Statistics Arise from Interference Effects.

The Keldysh-ordered full counting statistics is a quasiprobability distribution describing the fluctuations of a time-integrated quantum observable. While it is well known that this distribution can fail to be positive, the interpretation and origin of this negativity has been somewhat unclear. Here, we show how the full counting statistics can be tied to trajectories through Hilbert space, and how this directly connects negative quasiprobabilities to an unusual interference effect. Our findings are illustrated with the example of energy fluctuations in a driven bosonic resonator; we discuss how negative quasiprobability here could be detected experimentally using superconducting microwave circuits.

Quantum Backaction Evading Measurement of Collective Mechanical Modes.

The standard quantum limit constrains the precision of an oscillator position measurement. It arises from a balance between the imprecision and the quantum backaction of the measurement. However, a measurement of only a single quadrature of the oscillator can evade the backaction and be made with arbitrary precision. Here we demonstrate quantum backaction evading measurements of a collective quadrature of two mechanical oscillators, both coupled to a common microwave cavity. The work allows for quantum state tomography of two mechanical oscillators, and provides a foundation for macroscopic mechanical entanglement and force sensing beyond conventional quantum limits.

Quantum Nondemolition Measurement of a Quantum Squeezed State Beyond the 3 dB Limit.

We use a reservoir engineering technique based on two-tone driving to generate and stabilize a quantum squeezed state of a micron-scale mechanical oscillator in a microwave optomechanical system. Using an independent backaction-evading measurement to directly quantify the squeezing, we observe 4.7±0.9 dB of squeezing below the zero-point level surpassing the 3 dB limit of standard parametric squeezing techniques. Our measurements also reveal evidence for an additional mechanical parametric effect. The interplay between this effect and the optomechanical interaction enhances the amount of squeezing obtained in the experiment.

Preparation and detection of a mechanical resonator near the ground state of motion.

Cold, macroscopic mechanical systems are expected to behave contrary to our usual classical understanding of reality; the most striking and counterintuitive predictions involve the existence of states in which the mechanical system is located in two places simultaneously. Various schemes have been proposed to generate and detect such states, and all require starting from mechanical states that are close to the lowest energy eigenstate, the mechanical ground state. Here we report the cooling of the motion of a radio-frequency nanomechanical resonator by parametric coupling to a driven, microwave-frequency superconducting resonator. Starting from a thermal occupation of 480 quanta, we have observed occupation factors as low as 3.8 +/- 1.3 and expect the mechanical resonator to be found with probability 0.21 in the quantum ground state of motion. Further cooling is limited by random excitation of the microwave resonator and heating of the dissipative mechanical bath. This level of cooling is expected to make possible a series of fundamental quantum mechanical observations including direct measurement of the Heisenberg uncertainty principle and quantum entanglement with qubits.

Quantum-limited amplification via reservoir engineering.

We describe a new kind of phase-preserving quantum amplifier which utilizes dissipative interactions in a parametrically coupled three-mode bosonic system. The use of dissipative interactions provides a fundamental advantage over standard cavity-based parametric amplifiers: large photon number gains are possible with quantum-limited added noise, with no limitation on the gain-bandwidth product. We show that the scheme is simple enough to be implemented both in optomechanical systems and in superconducting microwave circuits.

Weak qubit measurement with a nonlinear cavity: beyond perturbation theory.

We analyze the use of a driven nonlinear cavity to make a weak continuous measurement of a dispersively coupled qubit. We calculate the backaction dephasing rate and measurement rate beyond leading-order perturbation theory using a phase-space approach which accounts for cavity noise squeezing. Surprisingly, we find that increasing the coupling strength beyond the regime describable by leading-order perturbation theory (i.e., linear response) allows one to come significantly closer to the quantum limit on the measurement efficiency. We interpret this behavior in terms of the non-Gaussian photon number fluctuations of the nonlinear cavity. Our results are relevant to recent experiments using superconducting microwave circuits to study quantum measurement.

Quantum signatures of the optomechanical instability.

In the past few years, coupling strengths between light and mechanical motion in optomechanical setups have improved by orders of magnitude. Here we show that, in the standard setup under continuous laser illumination, the steady state of the mechanical oscillator can develop a nonclassical, strongly negative Wigner density if the optomechanical coupling is comparable to or larger than the optical decay rate and the mechanical frequency. Because of its robustness, such a Wigner density can be mapped using optical homodyne tomography. This feature is observed near the onset of the instability towards self-induced oscillations. We show that there are also distinct signatures in the photon-photon correlation function g(2)(t) in that regime, including oscillations decaying on a time scale not only much longer than the optical cavity decay time but even longer than the mechanical decay time.

Cooling a nanomechanical resonator with quantum back-action.

Quantum mechanics demands that the act of measurement must affect the measured object. When a linear amplifier is used to continuously monitor the position of an object, the Heisenberg uncertainty relationship requires that the object be driven by force impulses, called back-action. Here we measure the back-action of a superconducting single-electron transistor (SSET) on a radio-frequency nanomechanical resonator. The conductance of the SSET, which is capacitively coupled to the resonator, provides a sensitive probe of the latter's position; back-action effects manifest themselves as an effective thermal bath, the properties of which depend sensitively on SSET bias conditions. Surprisingly, when the SSET is biased near a transport resonance, we observe cooling of the nanomechanical mode from 550 mK to 300 mK--an effect that is analogous to laser cooling in atomic physics. Our measurements have implications for nanomechanical readout of quantum information devices and the limits of ultrasensitive force microscopy (such as single-nuclear-spin magnetic resonance force microscopy). Furthermore, we anticipate the use of these back-action effects to prepare ultracold and quantum states of mechanical structures, which would not be accessible with existing technology.