Observing and Verifying the Quantum Trajectory of a Mechanical Resonator

Abstract

Continuous weak measurement allows localizing open quantum systems in state space, and tracing out their quantum trajectory as they evolve in time. Efficient quantum measurement schemes have previously enabled recording quantum trajectories of microwave photon and qubit states. We apply these concepts to a macroscopic mechanical resonator, and follow the quantum trajectory of its motional state conditioned on a continuous optical measurement record. Starting with a thermal mixture, we eventually obtain coherent states of 78% purity-comparable to a displaced thermal state of occupation 0.14. We introduce a retrodictive measurement protocol to directly verify state purity along the trajectory, and furthermore observe state collapse and decoherence. This opens the door to measurement-based creation of advanced quantum states, and potential tests of gravitational decoherence models.

Rapid cooling of a strain-coupled oscillator by an optical phase-shift measurement

“…The first, non-linear term in the equation for a 11 shows that the variance of X m is reduced, and the proportionality with the measurement efficiency η emphasizes that this squeezing of the oscillator position is conditional on the probing. The first term in the equation for a 22 shows that the unobserved P m undergoes an increasing variance due to the interaction with the probe field -a diffusive heating due to the spread in X ph of the incident state.…”

Quantum measurement engines and their relevance for quantum interpretations

“…Refs. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]). With the change of state, the disturbance of the system also implies a change of expectation values of observables.…”

Synchronization along quantum trajectories

“…The quantum trajectory approach describes the stochastic evolution of the pure state of the system of interest when environmental monitoring is available [40,41]. This formalism allows for a deeper notion of synchronization in the quantum regime, and enables to explore a hidden link between the emergence of synchronization and the generation of entanglement along single stochastic realizations of the process, which cannot be inferred from the density operators.The impressive development of experimental techniques in the last decade allowed the generation and recording of quantum trajectories in a number of platforms, including ultrahigh-Q Fabry-Perot cavities [42,43], superconducting qubits [44][45][46][47][48] and optomechanical systems [49,50]. Recently, Ref.[37] provided a first clue on the potential of quantum trajectories by using them to detect the presence of different phase-locking regimes.Here we aim to exploit at maximum the extra information that environmental measurements may offer us to give a deeper characterization of synchronization and phaselocking in the quantum regime.We consider one of the most paradigmatic setups for the study of quantum synchronization, namely, a couple of (self-sustained) Van der Pol (VdP) oscillators weakly interacting through a dissipative coupling [7,51].…”

“…The impressive development of experimental techniques in the last decade allowed the generation and recording of quantum trajectories in a number of platforms, including ultrahigh-Q Fabry-Perot cavities [42,43], superconducting qubits [44][45][46][47][48] and optomechanical systems [49,50]. Recently, Ref.…”