High-finesse Optical Resonator Research Articles

Optical cavity spectroscopy using heterodyne detection with optical feedback laser frequency locking.

We demonstrate an accurate high sensitivity method for cavity spectroscopy. We measure the frequency intervals of transverse electromagnetic modes relative to a fundamental mode in a high finesse optical resonator, and attribute their mode numbers unambiguously. A laser is frequency locked to a fundamental T E M 00 cavity mode by optical feedback, and phase modulation is used to obtain frequency side bands, which may come to resonance with other transverse cavity modes as the radio-frequency of the modulation is tuned. At these resonances, transmission of the side bands is sensitively detected by heterodyning with the carrier. We also analyze the transverse spatial profile of the heterodyne signal for identification of mode numbers. The adjustment of the Gaussian cavity model to the measured frequency intervals yields values of cavity length, mirror radius of curvature, and mirror ellipticity, with high precision to the ppm level.

Convolutional neural networks for mode on-demand high finesse optical resonator design

We demonstrate the use of machine learning through convolutional neural networks to solve inverse design problems of optical resonator engineering. The neural network finds a harmonic modulation of a spherical mirror to generate a resonator mode with a given target topology (“mode on-demand”). The procedure allows us to optimize the shape of mirrors to achieve a significantly enhanced coupling strength and cooperativity between a resonator photon and a quantum emitter located at the center of the resonator. In a second example, a double-peak mode is designed which would enhance the interaction between two quantum emitters, e.g., for quantum information processing.

Low frequency-to-intensity noise conversion in a pulsed laser cavity locking by exploiting carrier envelope offset

We report on the dependence of the frequency-to-intensity noise conversion in the locking of an ultrafast laser against a high-finesse optical enhancement resonator from the carrier envelope offset frequency. By a proper combination of the cavity finesse and laser carrier envelope offset frequency, it is possible to optimize the signal-to-noise ratio of the laser intensity trapped into the optical resonator. In this paper, we describe the effect of the laser-enhancement cavity coupling on the intracavity power relative noise, and we demonstrate both theoretically and experimentally its reduction.

Ultrasound sensing at thermomechanical limits with optomechanical buckled-dome microcavities.

We describe the use of monolithic, buckled-dome cavities as ultrasound sensors. Patterned delamination within a compressively stressed thin film stack produces high-finesse plano-concave optical resonators with sealed and empty cavity regions. The buckled mirror also functions as a flexible membrane, highly responsive to changes in external pressure. Owing to their efficient opto-acousto-mechanical coupling, thermal-displacement-noise limited sensitivity is achieved at low optical interrogation powers and for modest optical (Q ∼ 103) and mechanical (Q ∼ 102) quality factors. We predict and verify broadband (up to ∼ 5 MHz), air-coupled ultrasound detection with noise-equivalent pressure (NEP) as low as ∼ 30-100 µPa/Hz1/2. This corresponds to an ultrasonic force sensitivity ∼ 2 × 10-13 N/Hz1/2 and enables the detection of MHz-range signals propagated over distances as large as ∼ 20 cm in air. In water, thermal-noise-limited sensitivity is demonstrated over a wide frequency range (up to ∼ 30 MHz), with NEP as low as ∼ 100-800 µPa/Hz1/2. These cavities exhibit a nearly omnidirectional response, while being ∼ 3-4 orders of magnitude more sensitive than piezoelectric devices of similar size. Easily realized as large arrays and naturally suited to direct coupling by free-space beams or optical fibers, they offer significant practical advantages over competing optical devices, and thus could be of interest for several emerging applications in medical and industrial ultrasound imaging.

Optically Loaded Strontium Lattice Clock With a Single Multi-Wavelength Reference Cavity

We report on the realization of a new compact strontium optical clock using a 2-D magneto-optical-trap (2D-MOT) as cold atomic source and a multi-wavelength cavity as the frequency stabilization system. All needed optical frequencies are stabilized to a zero-thermal expansion high-finesse optical resonator and can be operated without frequency adjustments for weeks. We present the complete characterization of the apparatus. Optical control of the atomic source allows us to perform low-noise clock operation without atomic signal normalization. Long- and short-term stability tests of the clock have been performed for the <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">88</sup> Sr bosonic isotope by means of interleaved clock operation. Finally, we present the first preliminary accuracy budget of the system.

Fast Control of Atom-Light Interaction in a Narrow Linewidth Cavity.

We propose a method to exploit high-finesse optical resonators for light-assisted coherent manipulation of atomic ensembles, overcoming the limit imposed by the finite response time of the cavity. The key element of our scheme is to rapidly switch the interaction between the atoms and the cavity field with an auxiliary control process as, for example, the light shift induced by an optical beam. The scheme is applicable to other atomic species, both in trapped and free fall configurations, and can be adopted to control the internal and/or external atomic degrees of freedom. Our method will open new possibilities in cavity-aided atom interferometry and in the preparation of highly nonclassical atomic states.

Dynamical density wave order in an atom–cavity system

We theoretically and experimentally explore the emergence of a dynamical density wave (DW) order in a driven dissipative atom–cavity system. A Bose–Einstein condensate is placed inside a high finesse optical resonator and pumped sideways by an optical standing wave. The pump strength is chosen to induce a stationary superradiant checkerboard DW order of the atoms stabilized by a strong intracavity light field. We show theoretically that, when the pump is modulated with sufficient strength at a frequency ω d close to a systemic resonance frequency ω >, a dynamical DW order emerges, which oscillates at the two frequencies ω > and ω < = ω d − ω >. This order is associated with a characteristic momentum spectrum, also found in experiments in addition to remnants of the oscillatory dynamics presumably damped by on-site interaction and heating, not included in the calculations. The oscillating density grating, associated with this order, suppresses pump-induced light scattering into the cavity. Similar mechanisms might be conceivable in light-driven electronic matter.

Prior-damage dynamics in a high-finesse optical enhancement cavity.

An observation of prior-damage behavior inside a high-finesse optical resonator is reported. Intra-cavity average power drops appeared with magnitude and time scale depending on the power level. Increasing further the incident laser beam power led to irreversible damage of the cavity coupling mirror surface. The origin of this phenomenon is investigated with post mortem mirror surface imaging and analysis of the signals reflected and transmitted by the enhancement cavity. Scattering losses induced by surface deformation due to a hot-spot surface contaminant is found to be most likely the dominant physics process behind this phenomenon.

Cavity-induced superconducting and 4kF charge-density-wave states

We propose two experimental setups for fermionic atoms in a high-finesse optical resonator in which either a superconducting state with s-wave symmetry of the pairs or a 4k F charge density wave can self-organize. In order to stabilize the s-wave pairing, a two component attractively in- teracting fermionic gas is confined to a one dimensional chain structure by an optical lattice. The tunneling of the atoms along the chains is suppressed initially by an energy offset between neighbor- ing sites. A Raman transition using the cavity mode and a transversal pump laser then reintroduces a cavity-assisted tunneling. The feedback mechanism between the cavity field and the atoms leads to a spontaneous occupation of the cavity field and of a state of the fermionic atoms which is dominated by s-wave pairing correlations. Extending the setup to a quasi-one-dimensional ladder structure where the tunneling of atoms along the rungs of the ladder is cavity-assisted, the repul- sively interacting fermionic atoms self-organize into a 4k F charge density wave. We use adiabatic elimination of the cavity field combined with state-of-the-art density matrix renormalization group methods in finite systems in order to identify the steady state phases of the system.

Quantum Relaxation and Metastability of Lattice Bosons with Cavity-Induced Long-Range Interactions.

The coupling of cold atoms to the radiation field within a high-finesse optical resonator, an optical cavity, induces long-range interactions which can compete with an underlying optical lattice. The interplay between short- and long-range interactions gives rise to new phases of matter including supersolidity (SS) and density waves (DW), and interesting quantum dynamics. Here it is shown that for hard-core bosons in one dimension the ground state phase diagram and the quantum relaxation after sudden quenches can be calculated exactly in the thermodynamic limit. Remanent DW order is observed for quenches from a DW ground state into the superfluid (SF) phase below a dynamical transition line. After sufficiently strong SF to DW quenches beyond a static metastability line DW order emerges on top of remanent SF order, giving rise to a dynamically generated SS state. Our method to handle infinite- and short-range interactions in the infinite system size limit opens a way to solve exactly other Hamiltonians with infinite- and short-range interactions as well.

Tailoring the transverse mode of a high-finesse optical resonator with stepped mirrors

Enhancement cavities (ECs) seeded with femtosecond pulses have developed into the most powerful technique for high-order harmonic generation (HHG) at repetition rates in the tens of MHz. Here, we demonstrate the feasibility of controlling the phase front of the excited transverse eigenmode of a ring EC by using mirrors with stepped surface profiles, while maintaining the high finesse required to reach the peak intensities necessary for HHG. The two lobes of a mode of a 3.93 m long EC, seeded with a single-frequency laser, are delayed by 15.6 fs with respect to each other before a tight focus, and the delay is reversed after the focus. The tailored transverse mode exhibits an on-axis intensity maximum in the focus. Furthermore, the geometry is designed to generate a rotating wavefront in the focus when few-cycle pulses circulate in the EC. This paves the way to gating isolated attosecond pulses (IAPs) in a transverse manner (similarly to the attosecond lighthouse), heralding IAPs at repetition rates well into the multi-10 MHz range. In addition, these results promise high-efficiency harmonic output coupling from ECs in general, with an unparalleled power scalability. These prospects are expected to tremendously benefit photoelectron spectroscopy and extreme-ultraviolet frequency comb spectroscopy.

Decoherence-protected memory for a single-photon qubit

The long-lived, efficient storage and retrieval of a qubit encoded on a photon is an important ingredient for future quantum networks. Although systems with intrinsically long coherence times have been demonstrated, the combination with an efficient light-matter interface remains an outstanding challenge. In fact, the coherence times of memories for photonic qubits are currently limited to a few milliseconds. Here we report on a qubit memory based on a single atom coupled to a high-finesse optical resonator. By mapping and remapping the qubit between a basis used for light-matter interfacing and a basis which is less susceptible to decoherence, a coherence time exceeding 100 ms has been measured with a time-independant storage-and-retrieval efficiency of 22%. This demonstrates the first photonic qubit memory with a coherence time that exceeds the lower bound needed for teleporting qubits in a global quantum internet.

Highly accurate intensity factors of pure CO2 lines near 2 μm.

Line intensities for carbon dioxide are measured with a novel spectroscopic approach, assisted by an optical frequency comb synthesizer for frequency calibration purposes. The main feature of the spectrometer consists in the exploitation of optical feedback from a V-shaped high-finesse optical resonator to effectively narrow a distributed feedback diode laser at the wavelength of 2 μm. Laser-gas interaction takes place inside an isothermal cell, which is placed on the transmission from the cavity. High quality, self-calibrated, absorption spectra are observed in pure CO2 samples at different gas pressures, in coincidence with three lines of the R-branch of the ν1 + 2ν2 + ν3 band. Line intensities are determined using a global fitting approach in which a manifold of spectra are simultaneously analyzed across the range of pressures between 5 and 100 Torr, sharing a restricted number of unknown parameters. Various sources of uncertainty have been identified and carefully quantified, thus leading to an overall uncertainty ranging between 0.17% and 0.23%. The measured values are in a very good agreement with recent ab initio predictions.

Phases of cold atoms interacting via photon-mediated long-range forces

Atoms in high-finesse optical resonators interact via the photons they multiply scatter into the cavity modes. The dynamics is characterized by dispersive and dissipative optomechanical long-range forces, which are mediated by the cavity photons, and exhibits a steady state for certain parameter regimes. In standing-wave cavities the atoms can form stable spatial gratings. Moreover, their asymptotic distribution is a Maxwell–Boltzmann whose effective temperature is controlled by the laser parameters. In this work we show that in a two-mode standing-wave cavity the stationary state possesses the same properties and phases of the generalized Hamiltonian mean field model in the canonical ensemble. This model has three equilibrium phases: a paramagnetic, a nematic, and a ferromagnetic one, which here correspond to different spatial orders of the atomic gas and can be detected by means of the light emitted by the cavities. We further discuss perspectives for investigating in this setup the ensemble inequivalence predicted for the generalized Hamiltonian mean field model.

Active cancellation of acoustical resonances with an FPGA FIR filter.

We present a novel approach to enhancing the bandwidth of a feedback-controlled mechanical system by digitally canceling acoustical resonances (poles) and anti-resonances (zeros) in the open-loop response via an FPGA FIR filter. By performing a real-time convolution of the feedback error signal with an inverse filter, we can suppress arbitrarily many poles and zeros below 100 kHz, each with a linewidth down to 10 Hz. We demonstrate the efficacy of this technique by canceling the ten largest mechanical resonances and anti-resonances of a high-finesse optical resonator, thereby enhancing the unity gain frequency by more than an order of magnitude. This approach is applicable to a broad array of stabilization problems including optical resonators, external cavity diode lasers, and scanning tunneling microscopes and points the way to applying modern optimal control techniques to intricate linear acoustical systems.

Dissipative time evolution of a chiral state after a quantum quench

We investigate the dynamics of fermionic atoms in a high-finesse optical resonator after a sudden switch on of the coupling between the atoms and the cavity. The atoms are additionally confined by optical lattices to a ladder geometry. The tunneling mechanism on a rung of a ladder is induced by a cavity assisted Raman process. At long times after the quantum quench the arising steady state can carry a chiral current. In this work we employ exact diagonalization techniques on small system sizes to study the dissipative attractor dynamics after the quench towards the steady state and deviations of the properties of the steady state from predictions obtained by adiabatically eliminating the cavity mode.

A photon-photon quantum gate based on a single atom in an optical resonator.

That two photons pass each other undisturbed in free space is ideal for the faithful transmission of information, but prohibits an interaction between the photons. Such an interaction is, however, required for a plethora of applications in optical quantum information processing. The long-standing challenge here is to realize a deterministic photon-photon gate, that is, a mutually controlled logic operation on the quantum states of the photons. This requires an interaction so strong that each of the two photons can shift the other's phase by π radians. For polarization qubits, this amounts to the conditional flipping of one photon's polarization to an orthogonal state. So far, only probabilistic gates based on linear optics and photon detectors have been realized, because "no known or foreseen material has an optical nonlinearity strong enough to implement this conditional phase shift''. Meanwhile, tremendous progress in the development of quantum-nonlinear systems has opened up new possibilities for single-photon experiments. Platforms range from Rydberg blockade in atomic ensembles to single-atom cavity quantum electrodynamics. Applications such as single-photon switches and transistors, two-photon gateways, nondestructive photon detectors, photon routers and nonlinear phase shifters have been demonstrated, but none of them with the ideal information carriers: optical qubits in discriminable modes. Here we use the strong light-matter coupling provided by a single atom in a high-finesse optical resonator to realize the Duan-Kimble protocol of a universal controlled phase flip (π phase shift) photon-photon quantum gate. We achieve an average gate fidelity of (76.2 ± 3.6) per cent and specifically demonstrate the capability of conditional polarization flipping as well as entanglement generation between independent input photons. This photon-photon quantum gate is a universal quantum logic element, and therefore could perform most existing two-photon operations. The demonstrated feasibility of deterministic protocols for the optical processing of quantum information could lead to new applications in which photons are essential, especially long-distance quantum communication and scalable quantum computing.

Audio-Band Frequency-Dependent Squeezing for Gravitational-Wave Detectors.

Quantum vacuum fluctuations impose strict limits on precision displacement measurements, those of interferometric gravitational-wave detectors among them. Introducing squeezed states into an interferometer's readout port can improve the sensitivity of the instrument, leading to richer astrophysical observations. However, optomechanical interactions dictate that the vacuum's squeezed quadrature must rotate by 90° around 50Hz. Here we use a 2-m-long, high-finesse optical resonator to produce frequency-dependent rotation around 1.2kHz. This demonstration of audio-band frequency-dependent squeezing uses technology and methods that are scalable to the required rotation frequency and validates previously developed theoretical models, heralding application of the technique in future gravitational-wave detectors.

Precision Interferometric Measurements of Mirror Birefringence in High-Finesse Optical Resonators.

High-finesse optical resonators found in ultrasensitive laser spectrometers utilize supermirrors ideally consisting of isotropic high-reflectivity coatings. Strictly speaking, however, the optical coatings are often non-uniformly stressed during the deposition process and therefore do possess some small amount of birefringence. When physically mounted the cavity mirrors can be additionally stressed in such a way that large optical birefringence is induced. Here we report a direct measurement of optical birefringence in a two-mirror Fabry-Pérot cavity with R = 99.99 % by observing TEM00 mode beating during cavity decays. Experiments were performed at a wavelength of 4.53 μm, with precision limited by both quantum and technical noise sources. We report a splitting of δν = 618(1) Hz, significantly less than the intrinsic cavity linewidth of δcav ≈ 3 kHz. With a cavity free spectral range of 96.9 MHz, the equivalent fractional change in mirror refractive index due to birefringence is therefore Δn/n = 6.38(1) × 10-6.

Thermodynamics and dynamics of atomic self-organization in an optical cavity

Pattern formation of atoms in high-finesse optical resonators results from the mechanical forces of light associated with superradiant scattering into the cavity mode. It occurs when the laser intensity exceeds a threshold value, such that the pumping processes counteract the losses. We consider atoms driven by a laser and coupling with a mode of a standing-wave cavity and describe their dynamics with a Fokker-Planck equation, in which the atomic motion is semiclassical but the cavity field is a full quantum variable. The asymptotic state of the atoms is a thermal state, whose temperature is solely controlled by the detuning between the laser and the cavity frequency and by the cavity loss rate. From this result we derive the free energy and show that in the thermodynamic limit selforganization is a second-order phase transition. The order parameter is the field inside the resonator, to which one can associate a magnetization in analogy to ferromagnetism, the control field is the laser intensity, however the steady state is intrinsically out-of-equilibrium. In the symmetry-broken phase quantum noise induces jumps of the spatial density between two ordered patterns: We characterize the statistical properties of this temporal behaviour at steady state and show that the thermodynamic properties of the system can be extracted by detecting the light at the cavity output. The results of our analysis are in full agreement with previous studies, extend them by deriving a self-consistent theory which is valid also when the cavity field is in the shot-noise limit, and elucidate the nature of the selforganization transition.