We develop a rigorous theoretical framework for interaction-induced phenomena in the waveguide quantum electrodynamics (QED) driven by mechanical oscillations of the qubits. Specifically, we predict that the simplest set-up of two qubits, harmonically trapped over an optical waveguide, enables the ultrastrong coupling regime of the quantum optomechanical interaction. Moreover, the combination of the inherent open nature of the system and the strong optomechanical coupling leads to emerging parity-time (\PT) symmetry, quite unexpected for a purely quantum system without artificially engineered gain and loss. The $\mathcal{PT}$ phase transition drives long-living subradiant states, observable in the state-of-the-art waveguide QED setups.
Ultrastrong light-matter interaction in an optomechanical system can result in nonlinear optical effects such as photon blockade. The system-bath couplings in such systems play an essential role in observing these effects. Here we study the quantum coherence of an optomechanical system with a dressed-state master equation approach. Our master equation includes photon-number-dependent terms that induce dephasing in this system. Cavity dephasing, second-order photon correlation, and two-cavity entanglement are studied with the dressed-state master equation.
We propose a scheme for controlling a radio-frequency mechanical resonator at the quantum level using a superconducting qubit. The mechanical part of the circuit consists of a suspended micrometer-long beam that is embedded in the loop of a superconducting quantum interference device (SQUID) and is connected in parallel to a transmon qubit. Using realistic parameters from recent experiments with similar devices, we show that this configuration can enable a tuneable optomechanical interaction in the single-photon ultrastrong-coupling regime, where the radiation-pressure coupling strength is lar…
The mechanical properties of light have found widespread use in the manipulation of gas-phase atoms and ions, helping create new states of matter and realize complex quantum interactions. The field of cavity-optomechanics strives to scale this interaction to much larger, even human-sized mechanical objects. Going beyond the canonical Fabry-Perot cavity with a movable mirror, here we explore a new paradigm in which multiple cavity-optomechanical elements are wired together to form optomechanical circuits. Using a pair of optomechanical cavities coupled together via a phonon waveguide we demonst…
Optomechanical devices sensitively transduce and actuate motion of nanomechanical structures using light. Single--crystal diamond promises to improve the performance of optomechanical devices, while also providing opportunities to interface nanomechanics with diamond color center spins and related quantum technologies. Here we demonstrate dissipative waveguide--optomechanical coupling exceeding 35 GHz/nm to diamond nanobeams supporting both optical waveguide modes and mechanical resonances, and use this optomechanical coupling to measure nanobeam displacement with a sensitivity of $9.5$ fm/$\s…
We present a direct mapping between the quantum optomechanical problem of the atoms harmonically trapped in the vicinity of a chiral waveguide and a generalized quantum Rabi model and discuss the analogy between the self-organization of atomic chains in photonic structures and Dicke-like quantum phase transitions in the ultrastrong coupling regime. We extend the class of the superradiant phase transitions for the systems possessing $\mathbb{Z}_3$ rather than parity $\mathbb{Z}_2$ symmetry and demonstrate the emergence of the multicomponent Schrodinger cat ground states in these systems.
We present the basic ingredients of continuum optomechanics, i.e. the suitable extension of cavity-optomechanical concepts to the interaction of photons and phonons in an extended waveguide. We introduce a real-space picture and argue which coupling terms may arise in leading order in the spatial derivatives. This picture allows us to discuss quantum noise, dissipation, and the correct boundary conditions at the waveguide entrance. The connections both to optomechanical arrays as well as to the theory of Brillouin scattering in waveguides are highlighted. We identify the 'strong coupling regim…
We explore the possibility of achieving a significant nonlinear phase shift among photons propagating in nanoscale waveguides exploiting interactions among photons that are mediated by vibrational modes and induced through Stimulated Brillouin Scattering (SBS). We introduce a configuration that allows slowing down the photons by several orders of magnitude via SBS involving sound waves and two pump fields. We extract the conditions for maintaining vanishing amplitude gain or loss for slowly propagating photons while keeping the influence of thermal phonons to the minimum. The nonlinear phase a…
Josephson circuits provide a realistic physical setup where the light-matter fine structure constant can become of order one, allowing to reach a regime dominated by non-perturbative effects beyond standard quantum optics. Simple processes, such as spontaneous emission, thus acquire a many-body character, that can be tackled using a new description of the time-dependent state vector in terms of quantum-superposed coherent states. We find that spontaneous atomic decay at ultrastrong coupling leads to the emission of spectrally broad Schrödinger cats rather than of monochromatic single photons. …
We propose a versatile, free-space cavity optomechanics platform built from two photonic crystal membranes, one of which is freely suspended, and designed to form a microcavity less than one wavelength long. This cavity features a series of photonic bound states in the continuum that, in principle, trap light forever and can be favorably used together with evanescent coupling for realizing various types of optomechanical couplings, such as linear or quadratic coupling of either dispersive or dissipative type, by tuning the photonic crystal patterning and cavity length. Crucially, this platform…
Stimulated Brillouin scattering was recently observed in nanoscale silicon waveguides. Surprisingly, thermally-driven photon-phonon conversion in these structures had not yet been reported. Here, we inject an optical probe in a suspended silicon waveguide and measure its phase fluctuations at the output. We observe mechanical resonances around 8 GHz with a scattering efficiency of $10^{-5} \, \text{m}^{-1}$ and a signal-to-noise ratio of 2. The observations are in agreement with a theory of noise in these waveguides as well as with stimulated measurements. Our scheme may simplify measurements …
At low temperatures, microwave cavities are often preferred for the readout and control of a variety of systems. In this paper, we present design and measurements on an optomechanical device based on a 3-dimensional rectangular waveguide cavity. We show that by suitably modifying the electromagnetic field corresponding to the fundamental mode of the cavity, the equivalent circuit capacitance can be reduced to 29 fF. By coupling a mechanical resonator to the modified electromagnetic mode of the cavity, we achieved a capacitance participation ratio of 43 $\%$. We demonstrate an optomechanical co…
Ultrastrong coupling between light and matter has, in the past decade, transitioned from theoretical idea to experimental reality. It is a new regime of quantum light-matter interaction, going beyond weak and strong coupling to make the coupling strength comparable to the transition frequencies in the system. The achievement of weak and strong coupling has led to increased control of quantum systems and applications like lasers, quantum sensing, and quantum information processing. Here we review the theory of quantum systems with ultrastrong coupling, which includes entangled ground states wit…
We investigate polariton-phonon hybrid excitations, which describe the collective excitations of emitter-photon polaritons and vibrational phonons, in a periodic array of vibrating two-level emitters interacting with waveguide photons. We demonstrate the emergence of an interaction-induced quasiperiodic structure caused by the interplay between phonon scatterings and waveguide-mediated long-range couplings. This quasiperiodicity fundamentally changes the excitation characteristics in the subradiant regime, which feature an appearance of topological edge states and a transition between ergodic …
Optomechanical gradient forces arise from evanescent fields of guided waves in parallel photonic waveguides. When designed to be of attractive nature, they increase exponentially as the gap between the waveguides decreases. Moreover, the amplitude of the gradient force can be well controlled due to its linear dependence on the input laser power. Here, we propose to exploit the intrinsic nonlinear nature of the optomechanical gradient force to induce a tunable 3-wave coupling between the fundamental modes of two doubly clamped nanophotonic beams. For one of the beams having half the width of th…
We propose a scheme for enhancing the optomechanical coupling between microwave and mechanical resonators by up to seven orders of magnitude to the ultrastrong coupling limit in a circuit optomechanical setting. The tripartite system considered here consists of a Josephson junction Cooper-pair box that mediates the coupling between the microwave cavity and the mechanical resonator. The optomechanical coupling can be modified by tuning the gate charge and the magnetic flux bias of the Cooper-pair box which in turn affect the Josephson capacitance of the Cooper-pair box. We additionally show tha…
Polariton-mediated light-sound interaction is investigated through resonant Brillouin experiments in GaAs/AlAs multiple-quantum wells. Photoelastic coupling enhancement at exciton-polariton resonance reaches 105 at 30 K as compared to a typical bulk solid room temperature transparency value. When applied to GaAs based cavity optomechanical nanodevices, this result opens the path to huge displacement sensitivities and to novel ultrastrong-coupling cavity phenomena with optomechanical couplings g0 in the range of 100 THz.
We show that the electromagnetic forces generated by the excitations of a mode in graphene-based optomechanical systems are highly tunable by varying the graphene chemical potential, and orders of magnitude stronger than usual non-graphene-based devices, in both attractive and repulsive regimes. We analyze coupled waveguides made of two parallel graphene sheets, either suspended or supported by dielectric slabs, and study the interplay between the light-induced force and the Casimir-Lifshitz interaction. These findings pave the way to advanced possibilities of control and fast modulation for o…
We numerically study silicon waveguides on silica showing that it is possible to simultaneously guide optical and acoustic waves in the technologically important silicon on insulator (SOI) material system. Thin waveguides, or fins, exhibit geometrically softened mechanical modes at gigahertz frequencies with phase velocities below the Rayleigh velocity in glass, eliminating acoustic radiation losses. We propose slot waveguides on glass with telecom optical frequencies and strong radiation pressure forces resulting in Brillouin gains on the order of 500 and 50,000 1/(Wm) for backward and forwar…
Nanophononics has the potential for information transfer, in an analogous manner to its photonic and electronic counterparts. The adoption of phononic systems has been limited, due to difficulties associated with the generation, manipulation, and detection of phonons, especially at GHz frequencies. Existing techniques often require piezoelectric materials with an external radiofrequency excitation that are not readily integrated into existing CMOS infrastructures, while non-piezoelectric demonstrations have been inefficient. In this work, we explore the optomechanical generation of coherent ph…
A cavity quantum electrodynamical (QED) system beyond the strong-coupling regime is expected to exhibit intriguing quantum phenomena. Here we report a direct measurement of the photon-dressed qubit transition frequencies up to four photons by harnessing the same type of state transitions in an ultrastrongly coupled circuit-QED system realized by inductively coupling a superconducting flux qubit to a coplanar-waveguide resonator. This demonstrates a convincing observation of the photon-dressed Bloch-Siegert shift in the ultrastrongly coupled quantum system. Moreover, our results show that the p…
Acousto-optic interaction in optomechanical crystals allows unidirectional control of elastic waves over optical waves. However, as a result of this nonlinear interaction, infinitely many optical modes are born. This article presents an exact formulaion of coupled mode theory for interaction between elastic and photonic Bloch waves moving along an optomechanical waveguide. In general, an optical wavefront is strongly diffracted by an elastic wave in frequency and wavevector, and thus infinite modes with different frequencies and wavevectors appear. We discuss resonance and mode conversion cond…
So far, Brillouin scattering and cavity optomechanics were mostly disconnected branches of research -- although both deal with photon-phonon coupling. This begs for the development of a broader theory that contains both fields. Here, we derive the dynamics of optomechanical cavities from that of Brillouin-active waveguides. This explicit transition elucidates the link between phenomena such as Brillouin amplification and electromagnetically induced transparency. It proves that effects familiar from cavity optomechanics all have traveling-wave partners, but not vice versa. We reveal a close con…
Quantum oscillators in Gaussian states are often characterized by average occupation numbers that refer to a basis of eigenstates of the non-interacting oscillator Hamiltonian. We argue that quantum state purity is a more appropriate characteristic of such states, which can be applied to oscillators of any dimensionality. For a one-dimensional oscillator, the state purity is directly related to a thermal occupation number defined with respect to the number state basis in which the oscillator's quantum state is thermal. Thus, it naturally introduces a more versatile definition of an average occ…
We investigate superconducting interference device (SQUID) with two asymmetric Josephson junctions coupled to a mechanical resonator embedded in the loop of the SQUID. We quantize this system in the case when the frequency of the mechanical resonator is much lower than the cavity frequency of the SQUID and in the case when they are comparable. In the first case, the radiation pressure and cross-Kerr type interactions arise and are modified by asymmetry. Cross-Kerr type coupling is the leading term at the extremum points where radiation pressure is zero. In the second case, the main interaction…
We theoretically show that strong mechanical quantum squeezing in a linear optomechanical system can be rapidly generated through the dynamical instability reached in the far red-detuned and ultrastrong coupling regime. We show that this mechanism, which harnesses unstable multimode quantum dynamics, is particularly suited to levitated optomechanics, and we argue for its feasibility for the case of a levitated nanoparticle coupled to a microcavity via coherent scattering. We predict that for sub-millimeter-sized cavities the particle motion, initially thermal and well above its ground state, b…
We theoretically investigate the phenomenon of electromagnetically induced transparency (EIT) of a weak probe field in hybrid optomechanics with a single three-level ($Λ$-type) atomic system. We report that, in the presence of optomechanical coupling and two transition coupling parameters of three-level atom (TLA), there occurs three distinct multiple EIT windows in the probe absorption spectrum. Moreover, the switching of multiple windows into double and single EIT windows can be obtained by suitably tuning the system parameters. Furthermore, the probe transmission spectrum have been studied.…
We theoretically study a circuit QED architecture based on a superconducting flux qubit directly coupled to the center conductor of a coplanar waveguide transmission-line resonator. As already shown experimentally [Abdumalikov et al. Phys. Rev. B 78, 180502 (2008)], the strong coupling regime of cavity QED can readily be achieved by optimizing the local inductance of the resonator in the vicinity of the qubit. In addition to yielding stronger coupling with respect to other proposals for flux qubit based circuit QED, this approach leads to a qubit-resonator coupling strength g which does not sc…
In this article, we rigorously analyze the effects of the dispersion forces (Casimir and van der Waals forces) on a nano-optomechanical device based on a silicon waveguide and a silicon dioxide substrate, surrounded by air and driven by optical forces. The dispersion forces are calculated using a modified Lifshitz theory, in order to take into account the device thickness and material s dielectric permittivities, which are obtained from experimental optical data and validated by means of a rigorous 3D FDTD simulation. We also take into account the mechanical nonlinearity of the waveguide, whic…
The interaction of optical and mechanical modes in nanoscale optomechanical systems has been widely studied for applications ranging from sensing to quantum information science. Here, we develop a platform for cavity optomechanical circuits in which localized and interacting 1550 nm photons and 2.4 GHz phonons are combined with photonic and phononic waveguides. Working in GaAs facilitates manipulation of the localized mechanical mode either with a radio frequency field through the piezo-electric effect, or optically through the strong photoelastic effect. We use this to demonstrate a novel aco…
Confining photons in cavities enhances the interactions between light and matter. In cavity optomechanics, this enables a wealth of phenomena ranging from optomechanically induced transparency to macroscopic objects cooled to their motional ground state. Previous work in cavity optomechanics employed devices where ubiquitous structural disorder played no role beyond perturbing resonance frequencies and quality factors. More generally, the interplay between disorder, which must be described by statistical physics, and optomechanical effects has thus far been unexplored. Here, we demonstrate how…
Understanding large-scale interacting quantum matter requires dealing with the huge number of quanta that are produced by scattering even a few particles against a complex quantum object. Prominent examples are found from high energy cosmic ray showers to the optical or electrical driving of degenerate Fermi gases. We tackle this challenge in the context of many-body quantum optics, as motivated by the recent developments of circuit quantum electrodynamics at ultrastrong coupling. The issue of particle production is addressed quantitatively with a simple yet powerful concept rooted in the quan…
Controlling the dynamics of mechanical resonators is central to many quantum science and metrology applications. Optomechanical control of diamond resonators is attractive owing to diamond's excellent physical properties and its ability to host electronic spins that can be coherently coupled to mechanical motion. Using a confocal microscope, we demonstrate tunable amplification and damping of a diamond nanomechanical resonator's motion. Observation of both normal mode cooling from room temperature to 80K, and amplification into self--oscillations with $60\,μ\text{W}$ of optical power is observ…
Cavity optomagnonics has emerged as a promising platform for studying coherent photon-spin interactions as well as tunable microwave-to-optical conversion. However, current implementation of cavity optomagnonics in ferrimagnetic crystals remains orders of magnitude larger in volume than state-of-the-art cavity optomechanical devices, resulting in very limited magneto-optical interaction strength. Here, we demonstrate a cavity optomagnonic device based on integrated waveguides and its application for microwave-to-optical conversion. By designing a ferrimagnetic rib waveguide to support multiple…
We study the propagation of photons in a one-dimensional environment consisting of two non-interacting species of photons frustratingly coupled to a single spin-1/2. The ultrastrong frustrated coupling leads to an extreme mixing of the light and matter degrees of freedom, resulting in the disintegration of the spin and a breakdown of the "dressed-spin", or polaron, description. Using a combination of numerical and analytical methods, we show that the elastic response becomes increasingly weak at the effective spin frequency, showing instead an increasingly strong and broadband response at high…
This thesis studies the interaction between near-infrared light and gigahertz sound in nanoscale silicon waveguides. Chapter 2 introduces photon-phonon coupling and its theoretical description, describing basic mechanisms and developing a quantum field theory of the process. Chapter 3 explores the dynamical effects in both waveguides and cavities. It also proves a connection between the Brillouin gain coefficient and the vacuum coupling rate. Chapter 4 deals with the observation of Brillouin scattering in nanoscale silicon waveguides. The waveguides tightly confine $193 \, \text{THz}$ light an…
We demonstrate an optomechanical phase shifter. By electrostatically deflecting the nanofabricated mechanical structure, the effective index of a nearby waveguide is changed and the resulting phase shift is measured using an integrated Mach-Zehnder interferometer. Comparing to thermo-optical phase shifters, our device does not consume power in static operation and also it can operate over large frequency, wavelength, and power ranges. Operation in the MHz range and sub-$μ$s pulses are demonstrated.
We study the implementation of quantum state transfer protocols in phonon networks, where in analogy to optical networks, quantum information is transmitted through propagating phonons in extended mechanical resonator arrays or phonon waveguides. We describe how the problem of a non-vanishing thermal occupation of the phononic quantum channel can be overcome by implementing optomechanical multi- and continuous mode cooling schemes to create a 'cold' frequency window for transmitting quantum states. In addition, we discuss the implementation of phonon circulators and switchable phonon routers, …
