Pulsed Levitating Optomechanics Enables Preparation of Provably Non-Gaussian Quantum States

Levitated nanoparticles offer a compelling platform for exploring quantum mechanics, and researchers are now demonstrating a pathway to create specifically tailored quantum states within these tiny systems. F. Bemani, A. A. Rakhubovsky, and R. Filip are pioneering work in this area, developing techniques to generate non-Gaussian states in levitated nanoparticles using pulsed optomechanical interactions and sensitive photon detection. This achievement represents a significant step forward because creating and controlling non-Gaussian states is crucial for advancing quantum sensing, exploring fundamental questions of quantum mechanics, and potentially observing macroscopic quantum effects. The team’s approach offers a feasible method for preparing these states in a single mechanical mode, opening up new possibilities for harnessing the quantum properties of levitated nanoparticles for practical applications and fundamental research.

Preparing quantum non-Gaussian states is essential for both dynamics and measurement, and researchers have extensively analysed methods using nonlinear and time-varying potentials. This work explores pulsed optomechanical interactions combined with nonlinear photon detection techniques to create mechanical Fock states and confirm their quantum non-Gaussianity. The research also predicts conditions under which the optomechanical interaction can induce multiple-phonon additions, relevant for studying n-phonon states.

Nanoparticle Cooling and Quantum State Characterization

This document details the theoretical background and supporting data for a study focused on cooling a levitated nanoparticle to its quantum ground state and generating, then characterizing, non-classical states. The goal is to create states exhibiting quantum properties beyond those possible with classical physics, achieved through a combination of optical forces and measurement techniques. The research employs heralded state preparation, using measurements on auxiliary optical fields to indicate the preparation of a specific quantum state of the nanoparticle. Optomechanics studies the interaction between light and mechanical motion, specifically the vibration of the nanoparticle.

Levitation suspends the nanoparticle in a vacuum using optical forces, isolating it from environmental disturbances. Reaching the quantum ground state, the lowest possible energy state, is crucial for observing quantum effects. Non-classical states, like squeezed states and Fock states, cannot be described by classical physics. Squeezed states reduce uncertainty in one observable at the expense of another, while Fock states represent a definite number of vibrational quanta, known as phonons. Heralded measurement uses information from auxiliary systems, like photons, to understand the state of the nanoparticle without directly measuring it.

The theoretical framework includes the Hamiltonian, which describes the total energy of the system, and the Master Equation, which describes how the quantum state evolves over time, accounting for both coherent evolution and dissipation. Input-Output Theory relates the input and output fields of the optical system to the internal dynamics, and quantum noise represents the inherent uncertainty in measurements. These equations are fundamental to the theoretical analysis, allowing researchers to predict system behaviour and design cooling and state preparation protocols. The research also investigates non-classicality criteria, mathematical conditions to determine if a quantum state is non-classical, and the non-classical depth, a metric quantifying the degree of non-classicality. These criteria and metrics are essential for verifying the successful creation of non-classical states.

Levitated Nanoparticles Generate Non-Gaussian Mechanical States

This research demonstrates a method for creating approximate mechanical Fock states using levitated nanoparticles and pulsed optomechanical interactions combined with nonlinear photon detection. The team successfully explored how these interactions can generate multiple-phonon additions, confirming the non-Gaussianity of the resulting mechanical states and highlighting their potential for applications like sensing phase-randomized displacements. The purity of the generated states directly improves sensitivity to these displacements, with benefits largely realised by resolving only a few Fock states. The work establishes a pathway towards single-phonon control of quantum motion in levitated systems, both within optical cavities and in free space.

Researchers characterised the robustness of these non-Gaussian states against noise and decoherence, including thermal noise and inefficient photon detection. While verification of the states is more straightforward in cavity-based setups due to direct state transfer mechanisms, the methodology developed can be adapted for free-space systems. The team acknowledges that photon recoil currently limits the accuracy of heralding, and reducing this heating through adjustments to the trapping setup could enable more complex sequences of phonon additions and subtractions. Future research directions include exploring the interplay between these phonon-added states and unitary Gaussian squeezing achievable when the trap is switched off, as well as investigating more complex motional potentials beyond harmonic traps.