Hong-Ou-Mandel Interference between Two Deterministic Collective Excitations in an Atomic Ensemble

We demonstrate deterministic generation of two distinct collective excitations in one atomic ensemble, and we realize the Hong-Ou-Mandel interference between them. Using Rydberg blockade we create single collective excitations in two different Zeeman levels, and we use stimulated Raman transitions to perform a beam-splitter operation between the excited atomic modes. By converting the atomic excitations into photons, the two-excitation interference is measured by photon coincidence detection with a visibility of 0.89(6). The Hong-Ou-Mandel interference witnesses an entangled NOON state of the collective atomic excitations, and we demonstrate its two times enhanced sensitivity to a magnetic field compared with a single excitation. Our work implements a minimal instance of boson sampling and paves the way for further multimode and multiexcitation studies with collective excitations of atomic ensembles.

Figure 1

Conceptual diagram of HOM interference with collective excitations. First, a collective two-excitation state is generated in a single atomic ensemble. Afterwards, a $\pi /2$ Raman pulse coupling $|s1⟩$ and $|s2⟩$ applies a “beam-splitter” operation for the collective excitations, coupling ${|1,1⟩}_{S1,S2}$ to ${|2,0⟩}_{S1,S2}$ and ${|0,2⟩}_{S1,S2}$. The amplitudes contributing to the remaining state ${|1,1⟩}_{S1,S2}$ occupation interfere destructively and, as a consequence, a NOON state ($N=2$) is created.

Figure 2

Level scheme and experimental layout. (a) Two collective excitations $|1{⟩}_{S1}$ and $|1{⟩}_{S2}$ are generated sequentially via Rydberg blockade ($AB\to BC\to AB\to BD$). The single-photon detuning of the Rydberg excitation process is set to $\mathrm{\Delta }=-40\mathrm{MHz}$ relative to the intermediate state $|5P_{1/2},F^{\prime }=1,m_{F^{\prime }}=0⟩$. The Rabi frequencies for ($A$, $B$, $C$, $D$) are $2\pi \times (2,6,14,14)\mathrm{MHz}$, respectively. (b) A beam-splitter operation between the collective occupation of states $|s1⟩$ and $|s2⟩$ is realized via stimulated Raman transition. $R_1$ and $R_2$ are the Raman light fields and $|\pm {\mathrm{\Delta }}_R|\approx 407\mathrm{MHz}$. (c) To convert collective atomic excitations to single photons for detection, we sequentially apply read control fields ($E\to F$), resonant with different upper levels. A collective atomic excitation will return to the initial state $|g⟩$ emitting a single phase matched photon due to collective interference. (d) Experimental layout. Control beams are combined with beam splitters (BS) and dichroic mirrors (DM). One optional port for $R_2$ is used for observing the HOM dip. At the atom location, the beam waist is $\sim 7\mu \mathrm{m}$ for $A/B$, $55\mu \mathrm{m}$ for $C/D/E/F$, and $180\mu \mathrm{m}$ for $R_1/R_2$. The small angles between the beams are ${\theta }_1=6°$ and ${\theta }_2=3°$. The photons converted from the collective excitations ($P1$ and $P2$) are emitted in the phase-matching direction ($Z$), and collected with a single-mode fiber and detected subsequently with two single-photon detectors (SPD). HWP denotes the half-wave plate, QWP denotes the quarter-wave plate, and PBS denotes the polarizing beam splitter.

Figure 3

Rabi oscillation with one or two collective excitations. (a) A single collective excitation ${|1⟩}_{S2}$ is prepared, and the read-out signal oscillates as a function of the Raman pulse duration. Counts of photons from ${|1⟩}_{S1}$ is relatively small due to low excitation-to-photon conversion efficiency. We fit the data with a damped oscillation function, which calibrates the Raman Rabi frequency to be $2\pi \times 1.626(5)\mathrm{MHz}$. (b) When both collective modes are excited in the state ${|1,1⟩}_{S1,S2}$, the $\{1,1\}$ photon coincidence signal also oscillates as a function of Raman pulse durations. We fit the data with a damped oscillation function, which results in an oscillation frequency of $2\pi \times 3.23(4)\mathrm{MHz}$ and coincidence dips at durations of a $\pi /2$ and a $3\pi /2$ pulse. In both plots the error bars are deduced by assuming that photon counts follow a Poisson distribution.

Figure 4

Measurement of HOM dip. By tuning the separation angle between the Raman beams, we continuously modify the distinguishability between the collective excitations after beam splitting. At the position of $\theta \simeq 0$, the best indistinguishability is achieved and a HOM dip is observed. For each angle, the beam-splitting Raman pulse ($\pi /2$) is verified to give a fidelity better than 96%. The error bars are deduced by assuming that photon counts follow a Poisson distribution.

Figure 5

Ramsey interference with NOON states of collective excitations. (a) A single excitation of ${|1⟩}_{S1}$ is prepared. The read-out photons oscillate as a function of the time interval between the two $\pi /2$ pulses with a Larmor precession frequency of 1.401(1) MHz, which is consistent with the applied magnetic field. (b) The collective two-excitation state ${|1,1⟩}_{S1,S2}$ is prepared and produces a NOON state with $N=2$ after the first $\pi /2$ pulse. $\{0,2\}$ and $\{1,1\}$ coincidence measurements are performed, where $\{0,2\}$ denotes two photons from the atomic state $|s2⟩$ and $\{1,1\}$ denotes one photon from each of the two states $|s1⟩$ and $|s2⟩$. The oscillation frequency of the coincidence signals is 2 times faster than the intensity signal modulation from the single excited states. Because of a restriction by our instrumental setup, we can only make these measurements starting from $\delta t\ge 800\mathrm{ns}$, and the time of all our data points is shifted by 800 ns. In both plots the error bars are deduced by assuming that photon counts follow a Poisson distribution.