Motional Quantum Ground State of a Levitated Nanoparticle from Room Temperature

The possible quantum behavior of macroscopically sized objects has puzzled researchers since the early days of quantum theory Schrodinger (1935). It is still an open question whether quantum laws are universally valid or whether a classical, “macrorealistic” description of nature has to take over for sufficiently large systems Leggett and Garg (1985). One goal of macroscopic quantum experiments is to shed light on this question by observing and controlling quantum behaviour at macroscopic scales Leggett (2002); Arndt and Hornberger (2014). This task is becoming increasingly difficult as larger systems are harder to shield from environmental influences that may decohere the desired quantum phenomena Schlosshauer (2007). It has been suggested that levitation in high vacuum can provide a radically new platform for exploring macroscopic quantum phenomena Chang et al. (2010); Romero-Isart et al. (2010, 2011a). Levitation allows for sufficient isolation of the center-of-mass motion of solid-state objects, which enables a combination of quantum control with free-fall dynamics even at room temperature. Here we report a first relevant step by cooling an optically levitated solid, a silica sphere of 143nm diameter, by more than 7 orders of magnitude to its quantum ground state of motion in a room-temperature environment. We use cavity cooling by coherent scattering Delic et al. (2019); Windey et al. (2019), a technique originally developed in the context of atomic physics for laser cooling of atoms and molecules Horak et al. (1997); Vuletic and Chu (2000), to cool the particle motion along the cavity axis to $n_{x}=0.43\pm 0.03$ phonons, corresponding to a temperature of $12~\mu$K. We estimate ground state coherence times of approximately $7.6~\mu$s at the achieved background pressure of $10^{-6}$ mbar. This corresponds to 15 coherent oscillations within the optical trap, which can be further improved by going to ultra-high vacuum. The demonstration of a pure quantum state of motion of a levitated solid-state object with $10^{8}$ atoms ($2\times 10^{9}$ a.m.u.) in a room temperature environment paves the way for generating and controlling manifestly non-classical states of complex and massive objects at unprecedented scales. This creates new opportunities for sensing applications and tests of fundamental physics.

Optical levitation of dielectric particles works by using forces induced by laser light that are strong enough to overcome gravity Ashkin (2006). At its most fundamental level, an incoming laser polarizes the dielectric material, which in turn interacts with the radiation field of the laser. As a consequence, a particle in a tightly focused laser beam experiences a gradient force towards the intensity maximum of the beam, resulting in a three-dimensional confinement of the particle Ashkin et al. (1986). Such ”optical tweezers” have become a powerful tool to manipulate dielectric objects in isolation from other environments. For example, the ability to trap individual mesoscopic objects and even living specimen in liquid has made a lasting impact on the field of biology and biophysics Ashkin (2006); Svoboda and Block (1994). On the other hand, trapping of micron- and sub-micron sized particles in vacuum has allowed to address previously unexplored regimes for example in stochastic thermodynamics Gieseler and Millen (2018), force sensing Hempston et al. (2017); Ranjit et al. (2016), metrology Kuhn et al. (2017); Reimann et al. (2018) and laboratory scale cosmology experiments such as searches for dark matter and dark energy Rider et al. (2016). In the domain of quantum physics, optical trapping and cooling of atoms Phillips (1998) has enabled the study of individual atoms and quantum gases. It is also a fundamental technique for confining particles to optical lattice geometries for the study of many-body quantum phenomena Bloch et al. (2008); Bernien et al. (2017).

Based on these previous achievements it is natural to consider if a combination of optical levitation of relatively large solids in high vacuum together with the methods of quantum optics will allow for a completely new regime of macroscopic quantum physics. The proposals that have been put forward suggest exactly that Chang et al. (2010); Romero-Isart et al. (2010, 2011a); Barker and Shneider (2010). Laser cooling techniques should enable to prepare a levitated solid-state particle in its quantum ground state of motion Chang et al. (2010); Romero-Isart et al. (2010); Barker and Shneider (2010). The particle wavepacket can then be expanded and modified by a sequence of free fall, coherent manipulations and quantum measurement operations Romero-Isart et al. (2011a); Pino et al. (2018); Romero-Isart et al. (2011b). This results in previously unattainable macroscopic superposition states of massive objects.

A key requirement for entering this new regime is to prepare the particle wavepacket in a sufficiently pure quantum state, in this case, to cool its motion into the quantum ground state. One possibility is to monitor the particle motion with a sensitivity at or below the ground state size of the wavepacket and apply a feedback force to directly counteract the motion Mancini et al. (1998); Courty et al. (2001). Such feedback cooling to the quantum ground state has recently been demonstrated for harmonic modes of cryogenically cooled micromechanical membranes Rossi et al. (2018). In the context of levitated nanoparticles, feedback cooling has initially been introduced to provide stable levitation in high vacuum Gieseler et al. (2012); Li et al. (2011); Vovrosh et al. (2017). At present, feedback cooling is limited to approximately 4 motional quanta (phonons) RN3 (2019). A different approach is derived from laser cooling of atoms, where the absorption and re-emission of Doppler-shifted laser photons provides a velocity dependent scattering force Phillips (1998). The presence of an optical cavity modifies the electromagnetic boundary conditions for the scattered light, which can be used to tailor the scattering rates and allows for cooling of particles without an accessible internal level structure such as molecules or dielectric solids Horak et al. (1997); Vuletic and Chu (2000); Vuletic et al. (2001); Domokos et al. (2001). These cavity-cooling schemes have been used in the past to achieve ground state cooling of various systems ranging from individual atoms to cryogenically cooled modes of solid-state nano- and micromechanical oscillators in the context of cavity optomechanics Teufel et al. (2011); Chan et al. (2011); Aspelmeyer et al. (2014). Previous attempts to apply cavity cooling to levitated solids have proven challenging and cooling was limited to several hundred phonons Kiesel et al. (2013); Asenbaum et al. (2013); Millen et al. (2015); Meyer et al. (2019); Delić et al. (2019), mainly due to co-trapping associated with high intracavity photon number and the excessive laser phase noise heating at the low motional frequencies ($<1$ MHz) Meyer et al. (2019); Delić et al. (2019). We are applying a modified scheme – cavity cooling by coherent scattering Delic et al. (2019); Windey et al. (2019); Vuletic et al. (2001); Leibrandt et al. (2009) – which circumvents these shortcomings and enables direct ground-state cooling of a solid in a room-temperature environment.

We trap a spherical silica particle with a nominal diameter of $d=143\pm 4$ nm inside a vacuum chamber using an optical tweezer. A tightly focused laser beam (power in the focus: $P_{tw}\approx 400$ mW; wavelength $\lambda=1064$ nm; frequency $\omega_{tw}=2\pi c/\lambda$ ; $c$: vacuum speed of light) creates a three-dimensional harmonic potential for the particle motion with motional frequencies ($\Omega_{x},\Omega_{y},\Omega_{z})/2\pi\approx(305,275,80)$ kHz. We position the particle within an optical cavity (cavity finesse $\mathcal{F}\approx 73.000$; cavity linewidth $\kappa/2\pi=193\pm 4$ kHz; cavity frequency $\omega_{cav}=\omega_{tw}+\Delta$; $\Delta$: laser detuning), which collects the tweezer light scattered off the nanoparticle under approximately a right angle (FIG. 1a). The particle has sub-wavelength dimension and hence resembles to good approximation a dipole emitter – driven by the optical tweezer the particle coherently scatters dipole radiation predominantly orthogonal to the tweezer polarization axis. Motorized translation stages in the tweezer optics allow us to position the particle with an accuracy of a few nm with respect to the cavity axis (x-direction), such that the particle can be well localized within one period of the cavity standing wave field. To achieve optimal cooling along the cavity axis the particle needs to be located at an intensity minimum of the cavity standing wave field Delic et al. (2019); Windey et al. (2019). At that location the particle is ”dark” and accordingly all dipole scattering into the cavity mode is inhibited due to destructive interference imposed by the cavity. The particle motion breaks this symmetry and therefore only inelastically scattered Stokes- and anti-Stokes photons at sideband frequencies $\omega_{tw}\pm\Omega_{x}$ can propagate in the cavity.

Cavity cooling of the particle motion occurs because (Stokes-)scattering processes along the cavity, which increase the kinetic energy of the particle by $\hbar\Omega_{x}$ per photon, are suppressed, while (anti-Stokes-) scattering processes, which reduce the energy accordingly, are enhanced Aspelmeyer et al. (2014); Wineland and Itano (1979). This process is maximized at the optimal detuning $\Delta\approx\Omega_{x}$, where the anti-Stokes sideband becomes fully resonant with the cavity. A particle in its quantum ground state of motion cannot further reduce its energy, hence anti-Stokes scattering close to the ground state is fundamentally inhibited (FIG.1b,c). The resulting sideband asymmetry in the scattering rates is a direct measure of the temperature of the harmonic particle motion, which does not require calibration to a reference bathSafavi-Naeini et al. (2012). We observe these sidebands, which are modulated by the cavity envelopePeterson et al. (2016), using frequency-selective heterodyne detection of the cavity output, specifically by mixing it with a strong local oscillator field ($P_{LO}\approx 400~\mu$W) detuned from the tweezer laser by $\omega_{\mathrm{het}}/2\pi=10.2$ MHz (FIG. 2a). Independent measurements of the cavity linewidth $\kappa$ and the laser detuning $\Delta$ allow us to correct the detected sideband ratios for the cavity envelope (see Appendix), and hence to extract the motional temperature of the particle via the fundamental sideband asymmetry (FIG. 2b). For this method to work reliably, it is important to exclude all relevant influences of noise contributions to the sideband asymmetry Sudhir et al. (2017). We ensure this by confirming that the detection process is shot-noise limited and that both amplitude- and phase-noise contributions of the drive laser are negligible (see Appendix). Figure 2c shows the measured phonon number $n_{x}$ along the cavity axis for different laser detunings $\Delta$. For near optimal detuning of $\Delta/2\pi=315$ kHz, we observe a final occupation as low as $n_{x}=0.43\pm 0.03$, corresponding to a temperature of $12.2\pm 0.5~\mu$K and a ground-state probability of $70\pm 2\%$. Note that in contrast to previous quantum experiments involving cryogenically cooled solid-state oscillators, ground state cooling here is achieved in a room temperature environment.

The final occupation $n_{fin}$ along any direction is reached when the total heating rate $\Gamma_{x}$ is balanced by the cooling rate $n_{fin}\times\gamma$, where $\gamma$ is the linewidth of the motional sidebands Jain et al. (2016). For the resolved sideband regime ($\kappa<\Omega_{x}$) as studied here, and in the absence of any other heating mechanisms, Stokes scattering due to the finite cavity linewidth limits cooling with optimal parameters to a minimum phonon occupation of $n_{min}=(\kappa/4\Omega_{x})^{2}\approx 0.025$. Note that in this case, detailed balance implies that the fundamental ground state asymmetry exactly compensates the effect of the cavity envelope and therefore both sidebands have equal power. Additional sources of heating are balanced by larger anti-Stokes scattering, which results in the overall observed sideband imbalance. By independently measuring nx and γ we extract a total heating rate as low as $\Gamma_{x}/2\pi=(20.6\pm 2.3)$ kHz at a pressure of $\sim 10^{-6}$ mbar. This is consistent with the separately measured heating rate due to background gas collisions Delić et al. (2019), $\Gamma_{gas}/2\pi=(16.1\pm 1.2)$ kHz and the expected heating contributions from photon recoil, $\Gamma_{rec}/2\pi\approx 6$kHz, and laser phase noise, $\Gamma_{phase}/2\pi<200$ Hz (see Appendix).

Using the measured heating rates we estimate a maximum coherence time of $(7.6\pm 1)~\mu$s in the optical trap, corresponding to approximately 15 coherent oscillations before populating the ground state with one phonon Chang et al. (2010); Romero-Isart et al. (2011b). In a free fall experiment, where the particle would be released from the optical trap, the dominant source for decoherence is the collision with a single background-gas molecule. Note that we are operating in an interesting transition regime, in which the initial ground-state wavepacket size is smaller than the thermal de Broglie wavelength of a gas molecule by a factor of $~6$ (see Appendix). In this so-called short-distance regime the decoherence rate increases quadratically with wavepacket size Romero-Isart (2011). As a consequence, a freely expanding wavepacket will experience smaller coherence times than expected from the measured ground state heating rates. At the achieved background pressure of $10^{-6}$ mbar, this limits the free-fall coherence time to $~1.4~\mu$s, which would allow for an expansion of the wavepacket by approximately a factor of 3, from the ground state size of $3.1$ pm to $10.2$ pm. For wavepacket sizes much larger than the de Broglie wavelength of a gas molecule the decoherence rate saturates in the so-called long-distance regime. Significantly larger wavepacket sizes can be achieved by decreasing this decoherence rate further, for example by operating at much lower pressures. Blackbody radiation will then become the dominant source of decoherence and will, for our room temperature parameters, allow for wavepacket expansions up to several nanometres. A wavepacket size on the order of the particle radius could be achieved by combining ultra-high vacuum (approximately $10^{-11}$ mbar) with cryogenic temperatures (below 130K) (see Appendix).

Our platform also entails the ability to manipulate the spatial profile of the trapping laser for implementing nonlinear potentials, and may open the possibility to create non-classical states of motion such as non-Gaussian states or large spatial superpositions. This is in stark contrast to current experiments that prepare motional quantum states using solid state harmonic oscillators, where coupling to external non-linear systems or measurements provide the interaction for non-classical state preparation O’Connell et al. (2010); Lee et al. (2011); Riedinger et al. (2016).

In conclusion, we have demonstrated ground-state cooling of a levitated solid-state object in a room temperature environment. The coherence time is limited by the background pressure of $10^{-6}$ mbar to $~7.6\mu$s, which constitutes a crucial step for the quantum state control of such massive solid-state systems. The inferred optomechanical coupling rate of $g_{x}/2\pi\approx 71$ kHz places the system well into the regime of strong cooperativity $C>1$, with $C=4g_{x}^{2}/(\kappa\Gamma_{x})\approx 5$, and should already allow to implement quantum optical protocols for the generation of non-classical states of motion Romero-Isart et al. (2011b); Leibfried et al. (2003). In future experiments, significant reduction of decoherence can be achieved mainly by lower background pressures, but potentially also by operating at lower temperatures and using smaller cavity mode volumes. The combination of cavity optomechanical quantum control of levitated systems and free fall experiments can open up a new class of macro-quantum physics, with potential applications also to quantum sensing Geraci et al. (2010); Degen et al. (2017) and other fields of fundamental physics Bateman et al. (2015). Most importantly, we believe that the quantum control of levitated systems is a viable route towards experiments in which quantum systems can act as gravitational source masses, as has been originally suggested by Feynman Rickles and DeWitt (2011) and recently been re-visited in the context of levitation Bose et al. (2017); Marletto and Vedral (2017).

Appendix