Scalable all-optical cold damping of levitated nanoparticles.

Motional control of levitated nanoparticles relies on either autonomous feedback via a cavity or measurement-based feedback via external forces. Recent demonstrations of the measurement-based ground-state cooling of a single nanoparticle employ linear velocity feedback, also called cold damping, and require the use of electrostatic forces on charged particles via external electrodes. Here we introduce an all-optical cold damping scheme based on the spatial modulation of trap position, which has the advantage of being scalable to multiple particles. The scheme relies on programmable optical tweezers to provide full independent control over the trap frequency and position of each tweezer. We show that the technique cools the centre-of-mass motion of particles along one axis down to 17 mK at a pressure of 2 × 10-6 mbar and demonstrate its scalability by simultaneously cooling the motion of two particles. Our work paves the way towards studying quantum interactions between particles; achieving three-dimensional quantum control of particle motion without cavity-based cooling, electrodes or charged particles; and probing multipartite entanglement in levitated optomechanical systems.

Encoding information in the mutual coherence of spatially separated light beams.

Coherence has been used as a resource for optical communications since its earliest days. It is widely used for the multiplexing of data, but not for the encoding of data. Here we introduce a coding scheme, which we call mutual coherence coding, to encode information in the mutual coherence of spatially separated light beams. We describe its implementation and analyze its performance by deriving the relevant figures of merit (signal-to-noise ratio, maximum bit-rate, and spectral efficiency) with respect to the number of transmitted beams. Mutual coherence coding yields a quadratic scaling of the number of transmitted signals with the number of employed light beams, which might have benefits for cryptography and data security.

Ponderomotive Squeezing of Light by a Levitated Nanoparticle in Free Space.

A mechanically compliant element can be set into motion by the interaction with light. In turn, this light-driven motion can give rise to ponderomotive correlations in the electromagnetic field. In optomechanical systems, cavities are often employed to enhance these correlations up to the point where they generate quantum squeezing of light. In free-space scenarios, where no cavity is used, observation of squeezing remains possible but challenging due to the weakness of the interaction, and has not been reported so far. Here, we measure the ponderomotively squeezed state of light scattered by a nanoparticle levitated in a free-space optical tweezer. We observe a reduction of the optical fluctuations by up to 25% below the vacuum level, in a bandwidth of about 15 kHz. Our results are explained well by a linearized dipole interaction between the nanoparticle and the electromagnetic continuum. These ponderomotive correlations open the door to quantum-enhanced sensing and metrology with levitated systems, such as force measurements below the standard quantum limit.

Tip-Enhanced Stokes-Anti-Stokes Scattering from Carbyne.

Carbyne, a linear chain of carbon atoms, is the truly one-dimensional allotrope of carbon and the strongest known Raman scatterer. Here, we use tip-enhanced Raman scattering (TERS) to further enhance the Raman response of a single carbyne chain confined inside a double-walled carbon nanotube. We observe an increase of the anti-Stokes scattering by a factor of 3290 and a 22-fold enhancement of the anti-Stokes/Stokes ratio relative to far-field measurements. The power dependence of the anti-Stokes/Stokes ratio under TERS conditions is indicative of coherent Stokes-anti-Stokes scattering mediated by an excited phonon. The role of resonance effects and laser-induced heating are discussed and potential opportunities are outlined.

Sub-Kelvin Feedback Cooling and Heating Dynamics of an Optically Levitated Librator.

Rotational optomechanics strives to gain quantum control over mechanical rotors by harnessing the interaction of light and matter. We optically trap a dielectric nanodumbbell in a linearly polarized laser field, where the dumbbell represents a nanomechanical librator. Using measurement-based parametric feedback control in high vacuum, we cool this librator from room temperature to 240 mK and investigate its heating dynamics when released from feedback. We exclude collisions with residual gas molecules as well as classical laser noise as sources of heating. Our findings indicate that we observe the torque fluctuations arising from the zero-point fluctuations of the electromagnetic field.

Kovacs Memory Effect with an Optically Levitated Nanoparticle.

The understanding of the dynamics of nonequilibrium cooling and heating processes at the nanoscale is still an open problem. These processes can follow surprising relaxation paths due to, e.g., memory effects, which significantly alter the expected equilibration routes. The Kovacs effect can take place when a thermalization process is suddenly interrupted by a change of the bath temperature, leading to a nonmonotonic evolution of the energy of the system. Here, we demonstrate that the Kovacs effect can be observed in the thermalization of the center of mass motion of a levitated nanoparticle. The temperature is controlled during the experiment through an external source of white Gaussian noise that mimics an effective thermal bath at a temperature that can be changed faster than any relaxation time of the system. We describe our experiments in terms of the dynamics of a Brownian particle in a harmonic trap without any fitting parameter, suggesting that the Kovacs effect can appear in a large variety of systems.

Anti-Stokes Raman Scattering of Single Carbyne Chains.

We investigate the anti-Stokes Raman scattering of single carbyne chains confined inside double-walled carbon nanotubes. Individual chains are identified using tip-enhanced Raman scattering (TERS) and heated by resonant excitation with varying laser powers. We study the temperature dependence of carbyne's Raman spectrum and quantify the laser-induced heating based on the anti-Stokes/Stokes ratio. Due to its molecular size and its large Raman cross section, carbyne holds great promise for local temperature monitoring, with potential applications ranging from nanoelectronics to biology.

Quantum control of a nanoparticle optically levitated in cryogenic free space.

Tests of quantum mechanics on a macroscopic scale require extreme control over mechanical motion and its decoherence1-3. Quantum control of mechanical motion has been achieved by engineering the radiation-pressure coupling between a micromechanical oscillator and the electromagnetic field in a resonator4-7. Furthermore, measurement-based feedback control relying on cavity-enhanced detection schemes has been used to cool micromechanical oscillators to their quantum ground states8. In contrast to mechanically tethered systems, optically levitated nanoparticles are particularly promising candidates for matter-wave experiments with massive objects9,10, since their trapping potential is fully controllable. Here we optically levitate a femtogram (10-15 grams) dielectric particle in cryogenic free space, which suppresses thermal effects sufficiently to make the measurement backaction the dominant decoherence mechanism. With an efficient quantum measurement, we exert quantum control over the dynamics of the particle. We cool its centre-of-mass motion by measurement-based feedback to an average occupancy of 0.65 motional quanta, corresponding to a state purity of 0.43. The absence of an optical resonator and its bandwidth limitations holds promise to transfer the full quantum control available for electromagnetic fields to a mechanical system. Together with the fact that the optical trapping potential is highly controllable, our experimental platform offers a route to investigating quantum mechanics at macroscopic scales11.

Erratum: GHz Rotation of an Optically Trapped Nanoparticle in Vacuum [Phys. Rev. Lett. 121, 033602 (2018)].

This corrects the article DOI: 10.1103/PhysRevLett.121.033602.

Raman Scattering Cross Section of Confined Carbyne.

We experimentally quantify the Raman scattering from individual carbyne chains confined in double-walled carbon nanotubes. We find that the resonant differential Raman cross section of confined carbyne is on the order of 10-22 cm2 sr-1 per atom, making it the strongest Raman scatterer ever reported.

Motional Sideband Asymmetry of a Nanoparticle Optically Levitated in Free Space.

The hallmark of quantum physics is Planck's constant h, whose finite value entails the quantization that gave the theory its name. The finite value of h gives rise to inevitable zero-point fluctuations even at vanishing temperature. The zero-point fluctuation of mechanical motion becomes smaller with growing mass of an object, making it challenging to observe at macroscopic scales. Here, we transition a dielectric particle with a diameter of 136 nm from the classical realm to the regime where its zero-point motion emerges as a sizable contribution to its energy. To this end, we optically trap the particle at ambient temperature in ultrahigh vacuum and apply active feedback cooling to its center-of-mass motion. We measure an asymmetry between the Stokes and anti-Stokes sidebands of photons scattered by the levitated particle, which is a signature of the particle's quantum ground state of motion.

Cold Damping of an Optically Levitated Nanoparticle to Microkelvin Temperatures.

We implement a cold-damping scheme to cool one mode of the center-of-mass motion of an optically levitated nanoparticle in ultrahigh vacuum (10^{-8} mbar) from room temperature to a record-low temperature of 100 µK. The measured temperature dependence on the feedback gain and thermal decoherence rate is in excellent agreement with a parameter-free model. For the first time, we determine the imprecision-backaction product for a levitated optomechanical system and discuss the resulting implications for ground-state cooling of an optically levitated nanoparticle.

Rapid Flipping of Parametric Phase States.

We experimentally demonstrate flipping the phase state of a parametron within a single period of its oscillation. A parametron is a binary logic element based on a driven nonlinear resonator. It features two stable phase states that define an artificial spin. The most basic operation performed on a parametron is a bit flip between these two states. Thus far, this operation involved changing the energetic population of the resonator and therefore required a number of oscillations on the order of the quality factor Q. Our technique takes a radically different approach and relies on rapid control of the underlying potential. Our work represents a paradigm shift for phase-encoded logic operations by boosting the speed of a parametron bit flip to its ultimate limit.

GHz Rotation of an Optically Trapped Nanoparticle in Vacuum.

We report on rotating an optically trapped silica nanoparticle in vacuum by transferring spin angular momentum of light to the particle's mechanical angular momentum. At sufficiently low damping, realized at pressures below 10^{-5} mbar, we observe rotation frequencies of single 100 nm particles exceeding 1 GHz. We find that the steady-state rotation frequency scales linearly with the optical trapping power and inversely with pressure, consistent with theoretical considerations based on conservation of angular momentum. Rapidly changing the polarization of the trapping light allows us to extract the pressure-dependent response time of the particle's rotational degree of freedom.

Sensing Static Forces with Free-Falling Nanoparticles.

Miniaturized mechanical sensors rely on resonant operation schemes, unsuited to detect static forces. We demonstrate a nanomechanical sensor for static forces based on an optically trapped nanoparticle in vacuum. Our technique relies on an off-resonant interaction of the particle with a weak static force, and a resonant readout of the displacement caused by this interaction. We demonstrate a sensitivity of 10 aN to static gravitational and electric forces. Our work provides a tool for the closer investigation of short-range forces, and marks an important step towards the realization of matter-wave interferometry with macroscopic objects.

Calibration and energy measurement of optically levitated nanoparticle sensors.

Optically levitated nanoparticles offer enormous potential for precision sensing. However, as for any other metrology device, the absolute measurement performance of a levitated-particle sensor is limited by the accuracy of the calibration relating the measured signal to an absolute displacement of the particle. Here, we suggest and demonstrate calibration protocols for levitated-nanoparticle sensors. Our calibration procedures include the treatment of anharmonicities in the trapping potential, as well as a protocol using a harmonic driving force, which is applicable if the sensor is coupled to a heat bath of unknown temperature. Finally, using the calibration, we determine the center-of-mass temperature of an optically levitated particle in thermal equilibrium from its motion and discuss the optimal measurement time required to determine the said temperature.

Cooling Mechanical Oscillators by Coherent Control.

In optomechanics, electromagnetic fields are harnessed to control a single mode of a mechanically compliant system, while other mechanical degrees of freedom remain unaffected due to the modes' mutual orthogonality and high quality factor. Extension of the optical control beyond the directly addressed mode would require a controlled coupling between mechanical modes. Here, we introduce an optically controlled coupling between two oscillation modes of an optically levitated nanoparticle. We sympathetically cool one oscillation mode by coupling it coherently to the second mode, which is feedback cooled. Furthermore, we demonstrate coherent energy transfer between mechanical modes and discuss its application for ground-state cooling.

Modulation of optical spatial coherence by surface plasmon polaritons.

The interference pattern observed in Young's double-slit experiment is intimately related to the statistical correlations of the waves emitted by the slits. As the waves in the slits become more correlated, the visibility of the interference pattern increases. Here, we experimentally modulate the statistical correlations between the optical fields emitted by a pair of slits in a metal film. The interaction between the slits is mediated by surface plasmon polaritons and can be tuned by the slit separation, which allows us to either increase or decrease the spatial coherence of the emerging fields relative to that of the incoming fields.

Reduced Auger recombination in single CdSe/CdS nanorods by one-dimensional electron delocalization.

Progress to reduce nonradiative Auger decay in colloidal nanocrystals has recently been made by growing thick shells. However, the physics of Auger suppression is not yet fully understood. Here, we examine the dynamics and spectral characteristics of single CdSe-dot-in-CdS-rod nanocrystals. These exhibit blinking due to charging/discharging, as well as trap-related blinking. We show that one-dimensional electron delocalization into the rod-shaped shell can be as effective as a thick spherical shell at reducing Auger recombination of the negative trion state.