Preparation and Decay of a Single Quantum of Vibration at Ambient Conditions

A single quantum of excitation of a mechanical oscillator is a textbook example of the principles of quantum physics. But mechanical oscillators, despite their pervasive presence in nature and modern technology, do not generically exist in an excited Fock state. In the past few years, careful isolation of gigahertz-frequency nanoscale oscillators has allowed experimenters to prepare such states at millikelvin temperatures. These developments illustrate the tension between the basic predictions of quantum mechanics—which should apply to all mechanical oscillators even at ambient conditions—and the extreme conditions required to observe those predictions. We resolve the tension by creating a single Fock state of a 40-THz vibrational mode in a crystal at room temperature and atmospheric pressure. After exciting a bulk diamond with a femtosecond laser pulse and detecting a Stokes-shifted photon, the Raman-active vibrational mode is prepared in the Fock state $|1⟩$ with 98.5% probability. The vibrational state is then mapped onto the anti-Stokes sideband of a subsequent pulse, which when subjected to a Hanbury Brown–Twiss intensity correlation measurement reveals the sub-Poisson number statistics of the vibrational mode. By controlling the delay between the two pulses, we are able to witness the decay of the vibrational Fock state over its 3.9-ps lifetime at ambient conditions. Our technique is agnostic to specific selection rules, and should thus be applicable to any Raman-active medium, opening a new general approach to the experimental study of quantum effects related to vibrational degrees of freedom in molecules and solid-state systems.

Popular Summary

While the physical properties of light are accurately described by indivisible units (the quanta) of energy known as photons, quantum mechanics predicts that mechanical vibrational energy is also quantized into fundamental units called phonons. This means that any vibrating object may gain or lose energy only by exchanging individual phonons. However, this discrete on-and-off behavior conflicts with our common experience of vibrating objects and, until now, single phonons have been observed only at extremely low temperature and under high vacuum. In our experiment, we show that a single phonon can be excited and detected at room temperature and in the air, bringing quantum behavior closer to our daily life.

To detect single quanta of vibration (single phonons), we shoot ultrafast laser pulses onto a diamond crystal to excite an internal vibration. Every so often, one photon (out of the billion or more from the laser) triggers a crystal vibration, creating a phonon and a new photon at a lower frequency. Using a single-photon detector, we record the creation of this photon. To prove that a single phonon is indeed created, we send a second laser pulse into the crystal and look for the reverse process: a photon and the phonon combining to spit out another photon at a higher frequency.

Our work opens exciting perspectives in the study of quantum phenomena in other naturally occurring materials and molecular systems and could have applications in ultrafast quantum technologies.

Figure 1

Concept of the experiment. (a) When monochromatic light reflects from an oscillating mirror, it acquires two Raman sidebands due to phase modulation (to first order in interaction strength). (b) When light interacts with a polarizable oscillator, whose induced polarization ${\overrightarrow{p}}_{\mathrm{ind}}$ depends on its internal coordinate $x_{\nu }$, it undergoes a phase modulation at the oscillator frequency, leading to the appearance of Stokes and anti-Stokes Raman sidebands in the scattered light. The anti-Stokes/Stokes intensity ratio is proportional to $\overline{n}/(\overline{n}+1)$, where $\overline{n}$ is the mean excitation number (or occupancy) of the vibrational mode. (c) Time evolution of a single repetition of the experiment showing the interaction of the write pulse, the subsequent detection of Stokes photons for heralding, and the final read pulse followed by measurement of two-photon correlation in the emitted anti-Stokes light. (d) Evolution of the probability $P(n)$ of finding the vibrational mode in the $n$th energy eigenstate during the different steps. The system is initially in a thermal state with $\overline{n}=1.5\times {10}^{-3}$ (for a mode frequency of 40 THz at 295 K). After the write pulse, the marginal state of the vibration is also thermal with $\overline{n}=[p/(1-p)]={10}^{-2}$ in this example (here $p$ is the interaction probability). Finally, after heralding, the distribution becomes peaked at $n=1$. The residual vacuum component is due to detection noise. For each distribution, we give the corresponding value of the vibrational mode’s intensity correlation function $g^{(2)}$.

Figure 2

Unconditional Stokes and anti-Stokes correlations. Two-photon coincidence histograms of the Stokes field ${\widehat{a}}_{\mathrm{S}}$ (write pulse energy 60 pJ, acquisition time 10 min) and anti-Stokes field ${\widehat{a}}_{\mathrm{AS}}$ (read pulse energy 372 pJ, acquisition time 60 min). For the anti-Stokes field the coincidences are recorded between the detectors measuring ${\hat{d}}_1$ and ${\hat{d}}_2$ as in Fig. 1, while the write pulse is blocked. For the measurement of the Stokes field, a beam splitter is added in the path of mode ${\widehat{a}}_{\mathrm{S}}$. The start-stop delay (horizontal axis) is scaled in multiples of the repetition period $\approx 12.5\mathrm{ns}$. After normalizing by the average number of accidental coincidences (the peaks at nonzero start-stop), the value at zero time delay represents the intensity correlation of the Stokes and anti-Stokes fields; namely, $g_{\mathrm{S}}^{(2)}(0)=2.0\pm 0.1$ and $g_{\mathrm{AS}}^{(2)}(0)=1.73\pm 0.11$. The hatched regions in gray, omitted in the analysis, are affected by spurious coincidences due to cross talk between the two detectors, which arise when hot-carrier-induced light emission from one detector [47] is received by the other detector.

Figure 3

Sub-Poissonian anti-Stokes statistics. Dependence of the heralded vibrational statistics on the write pulse energy and on the corresponding estimated probability of creating at least one Stokes photon per pulse, $n_{\mathrm{S}}=[p/(1-p)]$. The normalized Stokes–anti-Stokes correlations are shown as an inset. The write-read pulse delay is fixed at zero and the read pulse energy at 322 pJ. Statistical error bars are obtained from the square root of the total number of events. Blue lines are models (see Supplemental Material, Sec. V[42]), using the estimated detection efficiency (10%) and a relative efficiency of the read process (relative to the Stokes emission cross section) of 30% as the only two adjustable parameters (common to both panels).

Figure 4

Decay of vibrational Fock state. Measured Stokes–anti-Stokes correlations (a) and heralded vibrational mode intensity correlation (b) as a function of write-read delay. The measurements (full circles) are taken with a pulse energy of 62 pJ in the write pulse and 409 pJ in the read pulse, with an acquisition time of 60 min for all points except the one at $-6.3\mathrm{ps}$, which was acquired over 8 h. Statistical error bars are obtained using the method described in Ref. [17]. Full circles are measured data and blue lines are from the model; see main text and Eq. (11). The prediction from the model without the added noise on the anti-Stokes detectors is shown with a dashed line in (b). Green bands in panels (a) and (b) show the region where a nonclassical model is required to explain the observations; red bands indicate where a classical model suffices. (c) Fock state distribution of the conditional vibrational mode inferred from the data via our model.