A fast squeeze of mechanical motion
ETH Zurich researchers report squeezing one component of a levitated nanoparticle’s angular motion to 11(3) decibels below its zero-point variance in 250 nanoseconds. Their version 1 preprint, submitted September 11, describes a silica particle held by an optical tweezer inside a room-temperature vacuum chamber. A rapid change in the tweezer’s polarization briefly placed the particle in an unstable, inverted potential. That instability amplified fluctuations in one direction of the particle’s quantum phase space while compressing them in the other.
Squeezing does not remove quantum uncertainty. It redistributes it. One measurable quantity becomes more precise while its conjugate partner becomes less precise, preserving the uncertainty relation. This trade can be useful when a sensor depends primarily on one component of motion. The experiment shows that an inverted optical potential can produce that redistribution much faster than one cycle of the oscillator. It did not, however, demonstrate a more sensitive instrument, detect a new force or create a spatial superposition of the complete nanoparticle.
The oscillator was a rotating nanoparticle
The particle was an anisotropic cluster formed from silica nanospheres with a nominal diameter of 120 nanometers. Because it was not perfectly spherical, its long axis tended to align with the polarization of the trapping laser. Small angular departures from that alignment produced a restoring torque. The resulting back-and-forth rotation is called libration. It is analogous to a pendulum’s oscillation, although here the object is nanoscale, suspended by light and measured through its optical scattering.
The apparatus supported three distinct librational modes. The researchers concentrated on the fastest, which oscillated at approximately 810 kilohertz and described rotation in the optical tweezer’s focal plane. The particle was trapped with 1,550-nanometer light in a chamber maintained near 1 times 10^-9 millibar. Room-temperature operation therefore refers to the temperature of the apparatus, not operation in ordinary air. The experiment still required ultrahigh vacuum, a precision optical cavity, active stabilization and carefully calibrated detection.
Cooling prepared the quantum starting point
A thermal oscillator already carries random motion that can overwhelm quantum-scale fluctuations. Before applying the squeezing operation, the team coupled the selected librational mode to a high-finesse optical cavity. Coherent scattering preferentially removed energy from the mode, cooling it close to its quantum ground state. The authors report a steady-state occupation of 0.12(6) quanta. That low initial occupation was essential because an inverted potential would amplify thermal uncertainty along with the quantum fluctuations of interest.
The optical cavity served two roles. It prepared the low-energy state and helped researchers monitor the particle’s angular motion through homodyne detection of scattered light. That coupling also introduced a later limitation. Once the squeezed particle returned to its stable trap, continued cavity cooling drove both the compressed and expanded components back toward the same steady-state variance. The preparation system was therefore also a source of relaxation, illustrating how a tool that creates a useful quantum state can shorten its lifetime.
Turning a trap upside down accelerated squeezing
With the tweezer polarized horizontally, the particle rested near the bottom of a stable angular potential. The researchers used a Pockels cell to rotate the polarization by 90 degrees. Its voltage pulse had a rise time of approximately 10 nanoseconds, much shorter than one libration period. Relative to the particle’s existing orientation, the change moved it from the bottom of the original potential to the top of an inverted one. Instead of restoring small deviations, the new potential drove them apart.
Evolution near that unstable point produces exponential rather than gradual separation in phase space. Fluctuations along one combined angular-position and angular-momentum direction grow, while those along the perpendicular direction shrink. The pulse duration controlled how long this squeezing continued. After 50, 150 or 250 nanoseconds, the team returned the polarization to its original direction, recapturing the particle in the stable potential before the instability could expel it from the useful region of the trap.
Repeated traces reconstructed the state
After recapture, the squeezed distribution rotated through phase space at the particle’s natural libration frequency. The researchers recorded its angular motion with homodyne detection and repeated the protocol 1,000 times for each inverted-potential duration. The experiment ran at one repetition per second so that the mechanical degrees of freedom could be cooled back to a consistent starting state. Combining many traces at different moments allowed the team to infer the covariance matrix describing the squeezed and anti-squeezed components.
The optical detector added photon shot noise to every trace. The researchers independently measured that imprecision and subtracted its variance before reporting the particle’s inferred angular variance. The strongest result, after a 250-nanosecond inverted-potential pulse, was 11(3) decibels of squeezing below the zero-point level. The conjugate component showed 13(1) decibels of anti-squeezing. The uncertainty product remained consistent, within the reported error bars, with its value after the initial cavity cooling.
Purity separated squeezing from added noise
A narrow distribution alone is not sufficient evidence of a high-quality squeezed state. A process might compress one direction while adding so much uncontrolled noise elsewhere that the overall state becomes highly mixed. The team therefore used the inferred covariance matrix to estimate purity, a measure that equals one for an ideal pure state and falls as uncontrolled uncertainty grows. At the maximum reported squeezing after 250 nanoseconds, the inferred purity was 0.74.
Up to that duration, the uncertainty product remained approximately constant within the measurement uncertainty, supporting the authors’ conclusion that the rapid squeezing step added little extra noise beyond the prepared starting state. The result still depends on calibrated shot-noise subtraction and a model of the oscillator’s harmonic evolution after recapture. It is not a direct image of a quantum wavefunction. Independent replication and alternative measurement methods would provide stronger evidence about the absolute squeezing and purity.
Longer pulses exposed technical noise
Keeping the particle in the inverted potential for longer did not continue improving the measured state. Beyond 250 nanoseconds, the squeezed variance departed from the expected exponential behavior and the inferred purity declined. The authors attribute the ceiling to a technical noise process. They suspect that another librational mode, which was not cooled as efficiently, heated during the longer pulse and disturbed the selected mode through nonlinear mechanical coupling. That mechanism is a proposed explanation, not a directly isolated cause.
Under a model containing only radiation-torque shot noise, the paper projects that substantially more squeezing could be possible at a longer pulse duration. The experiment did not reach that regime. Cooling all rotational modes more thoroughly may help, but it would add control requirements and must be tested. The observed degradation is important because an inverted potential magnifies unwanted disturbances as efficiently as it magnifies the controlled fluctuations used to generate squeezing. Faster state production helps only if alignment, mode coupling and optical noise remain controlled.
The squeezed state lasted about 30 cycles
The team followed the prepared state after returning the particle to the stable trap. The squeezed and anti-squeezed variances converged toward the cavity-cooled steady state with a reported decay time of approximately 38 microseconds. At the measured libration frequency, the nonclassical distribution persisted for about 30 oscillation periods. The researchers estimate that changing the cavity detuning after preparation could extend the lifetime, but that longer recoil-limited duration was not demonstrated.
A short-lived state can still be useful when a measurement fits inside its available window. The 250-nanosecond preparation time leaves room for control and sensing operations before the measured relaxation. Yet practical metrology would need a full protocol showing that the squeezed quadrature improves estimation of a real signal after preparation, readout noise and repetition time are counted. This study establishes the state-production mechanism and its measured lifetime, not an end-to-end sensing advantage.
A new control tool, with applications still ahead
The experiment’s clearest contribution is a fast, all-optical method for manipulating quantum mechanical motion in a levitated object. Switching polarization avoided the alignment sensitivity associated with combining separate optical and electrical potentials. The inverted trap generated squeezing in less than one fifth of the selected oscillator’s period, helping the operation outrun decoherence. Angular motion also provides a degree of freedom distinct from the center-of-mass motion more commonly studied in levitated systems.
The evidence remains a first-version preprint without peer review or independent reproduction. One particle and one librational mode do not establish scalability, long-term stability or usefulness in a deployed sensor. Nor does squeezing constitute a macroscopic superposition or a test that rules out alternative physical theories. The next step is to control the technical mode coupling, preserve the state longer and apply it to a defined measurement. For now, the result advances the mechanical quantum-control toolkit by showing that deliberate instability can prepare a strongly squeezed angular state before noise catches up.