Enhanced Energy Transfer to an Optomechanical Piston from Indistinguishable Photons

Thought experiments involving gases and pistons, such as Maxwell’s demon and Gibbs’ mixing, are central to our understanding of thermodynamics. Here, we present a quantum thermodynamic thought experiment in which the energy transfer from two photonic gases to a piston membrane grows quadratically with the number of photons for indistinguishable gases, while it grows linearly for distinguishable gases. This signature of bosonic bunching may be observed in optomechanical experiments, highlighting the potential of these systems for the realization of thermodynamic thought experiments in the quantum realm.

Figure 1

Illustration of an optomechanics setup to generalize a variety of classic thermodynamic experiments involving gases and piston membranes. The classical gases are realized by photon gases on either side of a movable beam-splitter membrane.

Figure 2

The correlation function ${\mathbb{g}}_{\mathrm{L,R}}$, Eq. (7), as a function of time for single photon, coherent, and thermal initial states of the light field in the absence of damping ($\kappa ={\kappa }_M=0$). Perfectly distinguishable ($\theta =\pi /2$), partially distinguishable ($\theta =\pi /4$), and perfectly indistinguishable ($\theta =0$) gases are denoted by solid, dashed, and dotted lines.

Figure 3

The Hong-Ou-Mandel effect in the present optomechanical setup. In diagram (a), the photon from the left is reflected and the photon from the right is transmitted, and vice versa in diagram (b). In diagram (c), both photons are transmitted, and in diagram (d), both are reflected. When the photons are perfectly distinguishable, i.e., $j=H$ and $k=V$ or vice versa, then all four outcomes (a)–(d) are equally probable. When the photons are perfectly indistinguishable, i.e., $j=H$ and $k=H$ or $j=V$ and $k=V$, then the amplitudes for outcomes (c) and (d) destructively interfere and the outcomes (a) and (b) are equally probable.

Figure 4

The average energy of the membrane as a function of time for coherent states of the light field containing $6\times {10}^6$ photons. Perfectly distinguishable, partially distinguishable, and perfectly indistinguishable gases are denoted by red, purple, and blue lines. We utilize the following parameters from the experimental settings in Refs. [20, 21]: ${\omega }_M=350\mathrm{kHz}$, $\omega =20\mathrm{THz}$, $\lambda =34\mathrm{GHz}$, $\kappa =85\mathrm{kHz}$, ${\kappa }_M=1\mathrm{Hz}$, $m=45\mathrm{ng}$, and $g{x}_{\mathrm{zpf}}=3.3\mathrm{kHz}$, with similar behavior expected for a range of parameters.