Optical Spring Effect Research Articles

Stable Optical Trap from a Single Optical Field Utilizing Birefringence.

We report a stable double optical spring effect in an optical cavity pumped with a single optical field that arises as a result of birefringence. One end of the cavity is formed by a multilayer Al_{0.92}Ga_{0.08}As/GaAs stack supported by a microfabricated cantilever with a natural mode frequency of 274Hz. The optical spring shifts the resonance to 21kHz, corresponding to a suppression of low frequency vibrations by a factor of about 5000. The stable nature of the optical trap allows the cavity to be operated without any external feedback and with only a single optical field incident.

Cavity optomechanical spring sensing of single molecules.

Label-free bio-sensing is a critical functionality underlying a variety of health- and security-related applications. Micro-/nano-photonic devices are well suited for this purpose and have emerged as promising platforms in recent years. Here we propose and demonstrate an approach that utilizes the optical spring effect in a high-Q coherent optomechanical oscillator to dramatically enhance the sensing resolution by orders of magnitude compared with conventional approaches, allowing us to detect single bovine serum albumin proteins with a molecular weight of 66 kDa at a signal-to-noise ratio of 16.8. The unique optical spring sensing approach opens up a distinctive avenue that not only enables biomolecule sensing and recognition at individual level, but is also of great promise for broad physical sensing applications that rely on sensitive detection of optical cavity resonance shift to probe external physical parameters.

Demonstration of an optical spring in the 100 g mirror regime

Optical rigidity will play an important role in future generations of gravitational wave (GW) interferometers which employ high laser power in order to reach and exceed the standard quantum limit. Several experiments have demonstrated the optical spring effect for very low weight mirror masses. In this paper we extend this to a mass and frequency regime more directly applicable to GW detectors. Using a end mirror mass we demonstrate an optical spring resonant at and a stiffness of 9.4 ×105 N m−1. The to mass regime may also be useful for the application as a readout mirror for optical bar or optical lever configurations.

An Optomechanical Elevator: Transport of a Bloch Oscillating Bose–Einstein Condensate up and down an Optical Lattice by Cavity Sideband Amplification and Cooling

In this paper we give a new description, in terms of optomechanics, of previous work on the problem of an atomic Bose–Einstein condensate interacting with the optical lattice inside a laser-pumped optical cavity and subject to a bias force, such as gravity. An atomic wave packet in a tilted lattice undergoes Bloch oscillations; in a high-finesse optical cavity the backaction of the atoms on the light leads to a time-dependent modulation of the intracavity lattice depth at the Bloch frequency which can in turn transport the atoms up or down the lattice. In the optomechanical picture, the transport dynamics can be interpreted as a manifestation of dynamical backaction-induced sideband damping/amplification of the Bloch oscillator. Depending on the sign of the pump-cavity detuning, atoms are transported either with or against the bias force accompanied by an up- or down-conversion of the frequency of the pump laser light. We also evaluate the prospects for using the optomechanical Bloch oscillator to make continuous measurements of forces by reading out the Bloch frequency. In this context, we establish the significant result that the optical spring effect is absent and the Bloch frequency is not modified by the backaction.

Position-Squared Coupling in a Tunable Photonic Crystal Optomechanical Cavity

We present the design, fabrication, and characterization of a planar silicon photonic crystal cavity in which large position-squared optomechanical coupling is realized. The device consists of a double-slotted photonic crystal structure in which motion of a central beam mode couples to two high-Q optical modes localized around each slot. Electrostatic tuning of the structure is used to controllably hybridize the optical modes into supermodes which couple in a quadratic fashion to the motion of the beam. From independent measurements of the anti-crossing of the optical modes and of the optical spring effect, the position-squared vacuum coupling rate is measured to be as large as 245 Hz to the fundamental in-plane mechanical resonance of the structure at 8.7MHz, which in displacement units corresponds to a coupling coefficient of 1 THz/nm$^2$. This level of position-squared coupling is approximately five orders of magnitude larger than in conventional Fabry-Perot cavity systems.

Observation of generalized optomechanical coupling and cooling on cavity resonance.

Optomechanical coupling between a light field and the motion of a cavity mirror via radiation pressure plays an important role for the exploration of macroscopic quantum physics and for the detection of gravitational waves (GWs). It has been used to cool mechanical oscillators into their quantum ground states and has been considered to boost the sensitivity of GW detectors, e.g., via the optical spring effect. Here, we present the experimental characterization of generalized, that is, dispersive and dissipative, optomechanical coupling, with a macroscopic (1.5 mm)2-size silicon nitride membrane in a cavity-enhanced Michelson-type interferometer. We report for the first time strong optomechanical cooling based on dissipative coupling, even on cavity resonance, in excellent agreement with theory. Our result will allow for new experimental regimes in macroscopic quantum physics and GW detection.

Torsional optical spring effect in coupled nanobeam photonic crystal cavities.

Compared to probe-tuned optomechanical cavity systems, coupled cavity systems have the merit of having much stronger optomechanical interactions. However, to date, the torsional optomechanical effects of coupled cavities have rarely been investigated. In this Letter, we report a torsional optical spring effect in coupled nanobeam photonic crystal cavities. One of the cavities is suspended by a multi-degree-of-freedom spring mechanism that supports torsional vibration modes. The cavities' light field acts in reverse on the selected torsional mode, thus generating a torsional optical spring effect. The experimental results show that the third-order torsional mode of the spring mechanism is optically stiffened and a maximum frequency increase of 77.1Hz is obtained. The device provides a novel configuration for the optomechanical design of a new degree of freedom (torsional motion) and the coupled cavities are favorable for strong optomechanical interactions in the torsional direction.

Optical spring effect in nanoelectromechanical systems

In this Letter, we report a hybrid system consisting of nano-optical and nano-mechanical springs, in which the optical spring effect works to adjust the mechanical frequency of a nanoelectromechanical systems resonator. Nano-scale folded beams are fabricated as the mechanical springs and double-coupled one-dimensional photonic crystal cavities are used to pump the “optical spring.” The dynamic characteristics of this hybrid system are measured and analyzed at both low and high input optical powers. This study leads the physical phenomenon of optomechanics in complex nano-opto-electro-mechanical systems (NOEMS) and could benefit the future applications of NOEMS in chip-level communication and sensing.

Nonlinear optomechanics in the stationary regime

We have observed nonlinear transduction of the thermomechanical motion of a nanomechanical resonator when detected as laser transmission through a sideband unresolved (stationary) optomechanical cavity. Nonlinear detection mechanisms are of considerable interest as special cases allow for quantum nondemolition measurements of the mechanical resonator's energy. We investigate the origin of the nonlinearity in the optomechanical detection apparatus and derive a theoretical framework for the nonlinear signal transduction, and the optical spring effect, from both nonlinearities in the optical transfer function and second-order optomechanical coupling. By measuring the dependence of the linear and nonlinear signal transduction---as well as the mechanical frequency shift---on laser detuning from optical resonance, we provide estimates of the contributions from the linear and quadratic optomechanical couplings.

Optically trapped mirror for reaching the standard quantum limit.

The preparation of a mechanical oscillator driven by quantum back-action is a fundamental requirement to reach the standard quantum limit (SQL) for force measurement, in optomechanical systems. However, thermal fluctuating force generally dominates a disturbance on the oscillator. In the macroscopic scale, an optical linear cavity including a suspended mirror has been used for the weak force measurement, such as gravitational-wave detectors. This configuration has the advantages of reducing the dissipation of the pendulum (i.e., suspension thermal noise) due to a gravitational dilution by using a thin wire, and of increasing the circulating laser power. However, the use of the thin wire is weak for an optical torsional anti-spring effect in the cavity, due to the low mechanical restoring force of the wire. Thus, there is the trade-off between the stability of the system and the sensitivity. Here, we describe using a triangular optical cavity to overcome this limitation for reaching the SQL. The triangular cavity can provide a sensitive and stable system, because it can optically trap the mirror's motion of the yaw, through an optical positive torsional spring effect. To show this, we demonstrate a measurement of the torsional spring effect caused by radiation pressure forces.

Cavity optomechanics in gallium phosphide microdisks

We demonstrate gallium phosphide (GaP) microdisk optical cavities with intrinsic quality factors >2.8 × 105 and mode volumes <10(λ/n)3, and study their nonlinear and optomechanical properties. For optical intensities up to 8.0 × 104 intracavity photons, we observe optical loss in the microcavity to decrease with increasing intensity, indicating that saturable absorption sites are present in the GaP material, and that two-photon absorption is not significant. We observe optomechanical coupling between optical modes of the microdisk around 1.5 μm and several mechanical resonances, and measure an optical spring effect consistent with a theoretically predicted optomechanical coupling rate g0/2π∼30 kHz for the fundamental mechanical radial breathing mode at 488 MHz.

Dynamics of a levitated nanosphere by optomechanical coupling and Casimir interaction

We discuss the dynamics of a hybrid optomechanical setup where a dielectric nanosphere is levitated inside the Fabry-P\'erot cavity of a standard optomechanical system with one movable cavity mirror. The nanosphere is coupled to the cavity field and the movable mirror by the optomechanical and Casimir interactions with coupling strengths being dependent on the distance between the levitated nanosphere and cavity mirror. We investigate the steady-state characteristics of the system and the optical spring effect of the nanosphere in detail. We also analyze the effects of the distance-dependent optomechanical coupling and Casimir interaction on the cooling of the levitated nanosphere in the cases of a movable and of a fixed cavity mirror. It is found that in both cases, ground-state cooling of the levitated nanosphere can be approached in a certain range of parameters. Furthermore, in contrast to the case with the fixed mirror, the cooling of the levitated nanosphere with a movable mirror can be optimized with a properly chosen mirror oscillation frequency.

Suppression of quantum-radiation-pressure noise in an optical spring

Recent advances in micro- and nanofabrication techniques have led to corresponding improvement in the performance of optomechanical systems, which provide a promising avenue towards quantum-limited metrology and the study of quantum behavior in macroscopic mechanical objects. One major impediment to reaching the quantum regime is thermal excitation, which can be overcome for a sufficiently high mechanical quality factor $Q$. Here, we propose a method for increasing the effective $Q$ of a mechanical resonator by stiffening it via the optical spring effect exhibited by linear optomechanical systems and show how the associated quantum-radiation-pressure noise can be evaded by sensing and feedback control. In a parameter regime that is attainable with current technology, this method allows for realistic quantum cavity optomechanics in a frequency band well below that which has been realized thus far.

Optomechanical effects of two-level systems in a back-action evading measurement of micro-mechanical motion

We show that the two-level systems (TLS) in lithographic superconducting circuits act as a power-dependent dielectric leading to non-linear responses in a parametrically coupled electromechanical system. Driven TLS shift the microwave resonance frequency and modulate the mechanical resonance through the optical spring effect. By pumping with two tones in a back-action evading measurement, these effects produce a mechanical parametric instability which limits single quadrature imprecision to 1.4 xzp. The microwave resonator noise is also consistent to a TLS-noise model. These observations suggest design strategies for minimizing TLS effects to improve ground-state cooling and quantum non-demolition measurements of motion.

Optical exchange spring effect in RF-annealed Fe-based amorphous ribbons

Abstract We report the surface exchange spring behavior in Fe-based amorphous ribbons which is detected by the magneto-optical Kerr effect. To realize this effect at the surface of FeSiB, the radio frequency (RF) radiation is used to change the magnetic phase of its outermost atomic surface layers. The RF radiation produced by a capacitively coupled parallel plate plasma reactor creates a nanometric hard magnetic layer on the surface of Fe-based ribbons and leaves the magnetically soft volume without any substantial modification.

Parametric optomechanical oscillations in two-dimensional slot-type high-Q photonic crystal cavities

We experimentally demonstrate an optomechanical cavity based on an air-slot photonic crystal cavity with optical quality factor Qo = 4.2 × 104 and a small modal volume of 0.05 cubic wavelengths. The optical mode is coupled with the in-plane mechanical modes with frequencies up to hundreds of MHz. The fundamental mechanical mode shows a frequency of 65 MHz and a mechanical quality factor of 376. The optical spring effect, optical damping, and amplification are observed with a large experimental optomechanical coupling rate gom/2π of 154 GHz/nm, corresponding to a vacuum optomechanical coupling rate g*/2π of 707 kHz. With sub-mW or less input power levels, the cavity exhibits strong parametric oscillations. The phase noise of the photonic crystal optomechanical oscillator is also measured.

Amplitude Noise Suppression in Cavity-Driven Oscillations of a Mechanical Resonator

We analyze the amplitude and phase noise of limit-cycle oscillations in a mechanical resonator coupled parametrically to an optical cavity driven above its resonant frequency. At a given temperature the limit-cycle oscillations have lower amplitude noise than states of the same average amplitude excited by a pure harmonic drive; for sufficiently low thermal noise a sub-Poissonian resonator state can be produced. We also calculate the linewidth narrowing that occurs in the limit-cycle states and show that while the minimum is set by direct phase diffusion, diffusion due to the optical spring effect can dominate if the cavity is not driven exactly at a sideband resonance.

A picogram- and nanometre-scale photonic-crystal optomechanical cavity

The dynamic back-action caused by electromagnetic forces (radiation pressure) in optical and microwave cavities is of growing interest. Back-action cooling, for example, is being pursued as a means of achieving the quantum ground state of macroscopic mechanical oscillators. Work in the optical domain has revolved around millimetre- or micrometre-scale structures using the radiation pressure force. By comparison, in microwave devices, low-loss superconducting structures have been used for gradient-force-mediated coupling to a nanomechanical oscillator of picogram mass. Here we describe measurements of an optical system consisting of a pair of specially patterned nanoscale beams in which optical and mechanical energies are simultaneously localized to a cubic-micron-scale volume, and for which large per-photon optical gradient forces are realized. The resulting scale of the per-photon force and the mass of the structure enable the exploration of cavity optomechanical regimes in which, for example, the mechanical rigidity of the structure is dominantly provided by the internal light field itself. In addition to precision measurement and sensitive force detection, nano-optomechanics may find application in reconfigurable and tunable photonic systems, light-based radio-frequency communication and the generation of giant optical nonlinearities for wavelength conversion and optical buffering.

Optical Dilution and Feedback Cooling of a Gram-Scale Oscillator to 6.9 mK

We report on the use of a radiation pressure induced restoring force, the optical spring effect, to optically dilute the mechanical damping of a 1 g suspended mirror, which is then cooled by active feedback (cold damping). Optical dilution relaxes the limit on cooling imposed by mechanical losses, allowing the oscillator mode to reach a minimum temperature of 6.9 mK, a factor of approximately 40 000 below the environmental temperature. A further advantage of the optical spring effect is that it can increase the number of oscillations before decoherence by several orders of magnitude. In the present experiment we infer an increase in the dynamical lifetime of the state by a factor of approximately 200.

Observation of optical spring effect in a microtoroidal optomechanical resonator

We present experimental evidence of the optical spring effect in a silica microtoroid resonator. The variation of the measured mechanical resonant frequency as a function of optical power, optical coupling, and optical detuning is in very good agreement with a model for radiation-pressure-induced rigidity in a silica microtoroid.