Measurement of a quantum system using spin-mechanical conversion

Abstract

Levitated macroscopic particles exhibiting quantum mechanical effects are garnering increased attention as a means for precision sensing and testing quantum mechanics. Defects in diamond, such as the nitrogen-vacancy (NV) centre possess optically-addressable spins with long coherence times at room temperature and offer an intriguing system to examine quantum spin dynamics coupled to a macroscopic classical particle. In this work, we convert the outcome of a quantum measurement on an ensemble of spins into a macroscopic rotation of the host particle via spin-mechanical coupling. Following a sequence of green laser and microwave control pulses, spin-mechanical coupling between the final qubit spin state and the host particle -- an electrically-levitated diamond -- exerts a torque on the particle that deflects a weak near-infra-red laser beam. We measure spin readout contrast in excess of 70\%, and demonstrate pulsed mechanical detection of coherent Rabi oscillations, spin-echo interferometry and $T_1$-induced relaxation. We directly measure with temporal resolution the particle reorientation from a 60\,attonewton-metre spin torque induced by flipping the spins. Our results open up interesting new opportunities for levitated spin-mechanical systems using pulsed control, from improved sensing to the prospect of realising macroscopic quantum superposition states.

Figures (10)

• Figure 1: Measurement via spin-mechanical conversion. a) Experimental schematic: a microdiamond with $\sim 10^8$ NV centres inside is levitated in a Paul trap. Quantum measurement: green light optically pumps NV centres inside the diamond into the $m_S = 0$ spin state, and a sequence of microwave pulses executes a quantum measurement on the spin ensemble. Spin-mechanical conversion: the projected outcome of the spin measurement results in a magnetisation that applies a torque to the levitated crystal. The crystal rotation is then measured by detecting scattered weak NIR light. b) cw-MDMR spectrum of scattered NIR light measured with continuous application of green, NIR and swept microwaves (sequence shown in (c), top). Only six of the eight resonances are visible here. We identify two resonances with opposite contrasts at $f_{1,2} = 2488, 3258\,$MHz corresponding to $m_S = 0\rightarrow\pm1$ spin transitions. c), bottom: pulsed-MDMR sequence: a 200-500 $\upmu$s 100 $\upmu$W green laser pulse optically pumps the NV centres, and a microwave pulse flips the target spin transition. Continuous application of non-perturbative NIR light facilitates readout of the motional transient induced by the mw pulse. d) Normalised NIR scatter for no mw pulse and $\pi$-pulses on the $f_{1,2}$ transitions. Grey dashed regions denote integration regions used in e), which shows mw Rabi oscillations on each spin transition and readout contrasts of 10-15%. Error bars deduced from photon counting statistics.
• Figure 2: SMC vs PL. a) SMC readout of Rabi oscillations averaged for 60 seconds, exhibiting 73(6) % measurement contrast, 50 times greater than Rabi oscillations detected via conventional PL measurements in 30 mins of averaging (inset, in orange). b), top: pulse sequence for mechanically-detected spin-echo, and bottom: results (10 min averaging), again compared with standard PL readout (inset, 33 min averaging). Error bars deduced from photon counting statistics.
• Figure 3: $T_1$ measurement via mechanical readout. a) Pulse sequence (top) and motional transient data vs delay time (bottom). The decay of the response is due to $T_1$ induced depolarisation, which attenuates the spin torque. Micromotion due to both the initial laser polarisation pulse and subsequent microwave $\pi$ pulse at the trap AC frequency is clearly evident, as well as mutual cancellation at multiples of $1/f_\text{trap}$. b) Detail, showing time traces vertically offset for clarity. The integrated signal response $F$ is plotted inset, from which $T_1$ may be determined.
• Figure 4: Pump-probe measurement of angular displacement. a) Schematic of experimental sequence and pertinent angles. A resonant 'pump' microwave $\pi$-pulse initiates reorientation of the diamond particle. After a time $t_d$, a second 'probe' $\pi$ pulse with varied frequency is applied: when resonant with the NV two-level splitting at the new diamond angle, the probe pulse arrests the spin-torque induced reorientation by repopulating the non-magnetic $m_S = 0$ state and drives the MDMR contrast towards unity. b) SMC contrast vs probe microwave frequency $f_2$ for different $t_d$ times, exhibiting a marked frequency shift in addition to amplitude suppression resulting from $T_1$-induced depolarisation. c) extracted contrast maximum position (points) and widths (shaded lines) vs evolution time $t_d$. Inset: the initial $100\,\upmu$s of evolution is given by $\theta(T) \approx 2\tau_\text{sp}/I t_d^2$, where $I$ is the moment of inertia, allowing the spin-induced torque $\tau_\text{sp}$ to be measured. Error bars in (c) extracted from standard error in fitted gaussian means.
• Figure S1: Schematic of the experimental setup. a) photograph of the Paul trap wire soldered to a printed circuit board, and b-d) images of trapped microdiamonds at different scales. In a), the scattered green light from a single particle is shown, in c) multiple particles are trapped, and in d) a high-magnification image of a single microdiamond is shown. Particles are illuminated with light flashed synchronously with the trap AC drive frequency to eliminate micromotion. e) Circuit to simultaneously apply high-voltage signal to Paul trap electrode and transmit microwaves. f) optical setup and beam paths. g) Power spectral density of particle motion measured via PMT and spectrum analyser, for a rotating particle (orange) and a librating particle (blue), traces vertically offset for clarity.