Two remote counting events induced by a single photon

Abstract

Motivated by Einstein's thought experiment that a single quantum particle diffracted after a pinhole could in principle produce an action in two or several places on a hemispherical imaging screen, here we explore theoretically the possibility to simultaneously detect the action of a single photon at two remote places. This is considered in a cascade quantum system composed of two spatially distant cavities each coupled to a qubit in the ultrastrong coupling regime. We show that a single-photon pulse incident on the two cavities can simultaneously excite the two remote qubits and lead to two subsequent single-photon detection events even when the separation between them is comparable to the spatial length of the photon pulse. Our results not only uncover new facets of photons at a fundamental level but also have practical applications, such as the generation of remote entanglement by a single photon through a dissipative channel which is otherwise unattainable in the strong-coupling regime.

Figures (3)

• Figure 1: (a) The original thought experiment proposed by Einstein, where a single quantum particle diffracted after a pinhole is then dispersed in space and detected at a hemispherical imaging screen of large radius. Einstein argued that the single quantum particle can produce an action at two or several places. (b) Our model to demonstrate that a single-photon pulse can simultaneously excite two remote qubits and lead to two subsequent single-photon detection events registered respectively by the detectors $D_{1}$ and $D_{2}$. Each qubit is coupled to a cavity in the USC regime, and the two qubit-cavity subsystems are unidirectionally and dissipatively coupled from the left to the right via the cavity decay $\kappa_{j}$. The separation between the two subsystems $d$ is considered comparable to the spatial length of the incident single-photon pulse $cT$ with $T$ and $c$ being its temporal duration and the speed of light respectively.
• Figure 2: (a) The eigenenergy spectrum of $\hat{H}$ as a function of $\omega_{c}/\omega_{q}$. The first six eigenstates are labeled by $|n\rangle$, and $|\pm\rangle\simeq (|gg10\rangle \pm |gg01)/\sqrt{2}$ for large $\omega_{c}/\omega_{q}$. (b) An enlarged view of the region denoted by the dashed circle in (a). There are two avoided crossings which indicates direct coupling between the states $|3\rangle$ and $|4\rangle$, and $|4\rangle$ and $|5\rangle$. (c) plots the excitation dynamics of each qubit, while the shaded region indicates the dimensionless mode function of the input photon pulse at the first cavity, i.e., $\sqrt{cT}u(x_{1}-ct)$. Here we have set $d=0$. (d) shows the second-order correlation between the two qubits for three different $d$. Here we have chosen parameters for the two subsystems as $\omega_{q1}=\omega_{q2}=\omega_{q}, \omega_{c1}=\omega_{c2}=\omega_{c},\theta_{1}=\theta_{2}=\theta,\eta_{1}=\eta_{2}=\eta, \gamma_{1}=\gamma_{2}=\gamma$. And $\eta = 0.5,\theta=\pi/5, G= 1.0, \kappa_{1}/\omega_{q} = 0.004,\kappa_{2}/\omega_{q}=0.001,T=1500/\omega_{q}$.
• Figure 3: (a) $C_{\text{max}}$ as a function of $\gamma$ for $d=0$ and $G=1$. (b) and (c) plot $C_{\text{max}}$ as a function of the distance $d$ and power gain factor $G$ respectively for $\gamma=0$. Other parameters are the same as in the caption of Fig. \ref{['fig2']}.