Interface between Trapped-Ion Qubits and Traveling Photons with Close-to-Optimal Efficiency

Experimental results are presented on the efficiency limits for a quantum interface between a matter-based qubit and a photonic qubit. Using a trapped ion in an optical cavity, we obtain a single ion-entangled photon at the cavity output with a probability of 0.69(3). The performance of our system is shown to saturate the upper limit to photon-collection probability from a quantum emitter in a cavity, set by the emitter’s electronic structure and by the cavity parameters. The probability for generating and detecting the ion-entangled fiber-coupled photon is 0.462(3), a fivefold increase over the previous best performance. Finally, the generation and detection of up to 15 sequential polarized photons demonstrates the ability of a trapped ion to serve as a multiphoton source. The comparison between measured probabilities and predicted bounds is relevant for quantum emitters beyond trapped ions, in particular, for the design of future systems optimizing photon collection from, and absorption in, quantum matter.

Popular Summary

A quantum version of the internet, built of interacting quantum light and matter, would enable powerful new capabilities for science and technology. A key requirement for the quantum internet is the ability to efficiently collect photons that are emitted by and entangled with quantum matter. In this work, we report on a significant increase in the efficiency of entangled photon collection from a leading example of quantum matter: a single trapped atomic ion. The achieved performance opens up new near-term methods for engineering and studying many-particle quantum states.

Our system, consisting of a trapped ion in the focus of an optical cavity, achieves close to the optimal compromise between the probability of a photon being emitted into the cavity mode and exiting through the output mirror. Furthermore, the achieved performance is shown to saturate recently developed theoretical limits, set only by the cavity and emitter parameters, allowing the paths to future efficiency improvements to be clearly identified. The comparison between measured probabilities and theoretical limits is relevant for quantum emitters beyond trapped ions, in particular, for the design of future systems optimizing photon collection from, and absorption in, quantum matter.

An intriguing outlook is to combine the multiqubit quantum-logic capabilities of the trapped-ion platform with the high-efficiency photon generation achieved in this work, to generate new many-body light-matter quantum states with widespread application. Indeed, as a first step in that direction we demonstrate here the detection of up to 15 sequential photons.

Figure 1

Limits to photon collection: a quantum emitter in a cavity. A three-level emitter in the waist $w_0$ of a vacuum mode of a cavity formed by two mirrors with transmission values $T_1$ and $T_2$. The unwanted cavity loss per round trip ${\alpha }_{\mathrm{loss}}$ includes $T_1$. The $|u⟩\leftrightarrow |e⟩$ transition is driven by an external field (blue arrow). The $|g⟩\leftrightarrow |e⟩$ transition is coupled to the cavity (red arrow). For the generation of photons, the system is initialized into the state $|u,0⟩$, where $|0⟩$ is the vacuum Fock state of the cavity. Emission of a photon into the cavity leaves the system in $|g,1⟩$. Spontaneous decay from $|e⟩$ to $|g⟩$ with decay constant ${\gamma }_g$ ends the attempt in failure, whereas decay from $|e⟩$ to $|u⟩$ with decay constant ${\gamma }_u$ allows for subsequent cavity photon generation (re-excitation processes). The maximum probability for a cavity photon to be emitted into the cavity and transmitted to the free-space output mode to the right of the cavity is given by Eq. (2) for $T_2^{\mathrm{opt}}$ and by Eq. (1) for an arbitrary $T_2$.

Figure 2

Experimental setup: photon generation from a trapped ion in a cavity. (a) A ${}^{40}{\mathrm{Ca}}^{+}$ ion in a linear Paul trap (shown electrodes are for radial, in plane, confinement) and at the focus, and a vacuum antinode, of an optical cavity. The vacuum Rabi frequency of the ion-cavity coupling is $g$. A drive laser pulse with Rabi frequency $\mathrm{\Omega }$ causes emission of an 854-nm photon into a vacuum mode of the cavity. $T_1$ and $T_2$ are mirror transmissions, ${\alpha }_{\mathrm{loss}}$ is the cavity round-trip loss, $P_S$ is the probability for obtaining a photon in the cavity output mode, $P_{\mathrm{el}}$ is the transmission of optical elements, $P_{\mathrm{FC}}$ is the fiber coupling efficiency, $P_{\det }$ is the detector efficiency. (b) Atomic level scheme showing the CMRT for photon generation. The cavity (red solid arrow) and drive laser (blue solid arrow) have a common detuning of $\mathrm{\Delta }/2\pi =-403(5)$ MHz from the excited state. Ground states other than $|g⟩$ and $|u⟩$ to which the excited state $|e⟩$ can decay are grouped in state $|o⟩$ (contained within the gray oval). The spontaneous decay rates are $({\gamma }_g,{\gamma }_u,{\gamma }_o)/2\pi =(0.45,10.74,0.30)$ MHz, with ${\gamma }_g+{\gamma }_u+{\gamma }_o=\gamma =2\pi 11.49$ MHz.

Figure 3

Single-photon wavepackets and efficiency. Histograms of photon arrival times for different Rabi frequencies $\mathrm{\Omega }/2\pi =[14(1),24(1),46(1)]$ MHz of the drive laser, normalized by the number of attempts $k=50000$ and by the time-bin width ${\delta }_t=(1.2,0.6,0.3)\mu \mathrm{s}$. Inset: integrated wavepackets, yielding efficiencies (averaged over a measurement time of about 8 min) $P_{\mathrm{tot}}=[0.490(3),0.478(3),0.437(3)]$. All plots: dots are experimental data, lines correspond to numerical simulations. Error bars correspond to one standard deviation based on Poissonian photon-counting statistics. Gray shaded area: $P_S^{\mathrm{exp.max}}\times P_{\mathrm{path}}$, i.e., maximum achievable total efficiency from the analytic model [calculated via Eq. (1)] given our detection-path efficiency.

Figure 4

Generation and characterization of the ion-photon entangled state. (a) Atomic level scheme showing the bichromatic CMRT that generates the ion-photon entangled state $|\mathrm{\Psi }(\theta )⟩=\frac{1}{\sqrt{2}}(|g_1⟩|V⟩+e^{i\theta }|g_2⟩|H⟩)$. The frequency difference of the detunings ${\mathrm{\Delta }}_1$ and ${\mathrm{\Delta }}_2$ is equal to the Zeeman splitting between $|g_1⟩=|D_{J=5/2},m_j=-5/2⟩$ and $|g_2⟩=|D_{J=5/2},m_j=-3/2⟩$. (b) Wavepackets in the $H/V$ (gray and black) polarization basis and their sum (green). The photon counts of all three ion-basis measurements are added up. Dots with error bars, measured data; lines, numerical simulations. Error bars represent one standard deviation, based on Poissonian photon statistics. Inset: integrated probabilities, yielding 0.224(4) for $H$ and 0.239(4) for $V$. (c) Data: real (top) and imaginary (bottom) part of the tomographically reconstructed density matrix $\rho$. (d) Theory: real (top) and imaginary (bottom) part of the density matrix of $|\mathrm{\Psi }(\theta =0.91)⟩$.

Figure 5

Photon trains: generation and detection of sequential photons (a) Measured wavepackets of 15 consecutive photon-generation attempts for the experimental configuration of Fig. 2 and $\mathrm{\Omega }/2\pi \approx 12$ MHz. (b) Temporal overlap of the first, fifth, and fifteenth wavepacket in (a). (c) Probability of detecting a photon in $n$ consecutive wavepackets, starting from the first wavepacket, for a single-photon probability of 0.47. Orange line: weighted fit of the form $p^x$, with $p=0.474(2)$ the best fit value.

Figure 6

${}^{40}{\mathrm{Ca}}^{+}$ level scheme with branching ratios and additional transitions used for cooling. Total decay of $P_{3/2}$ [39]: $\gamma /2\pi =11.49(3)$ MHz. Branching ratios [61]: $r_{D1/2}=0.9347(3)$, $r_{D3/2}=0.00661(4)$, $r_{D5/2}=0.0587(2)$.

Figure 7

Predicted photon probabilities in our system as a function of the output-mirror transmission $T_2$. The probability for obtaining a photon in the output mode of the cavity $P_S=P_{\mathrm{esc}}{P}_{\mathrm{in}}$ results from the product of the probability for photon emission into the cavity $P_{\mathrm{in}}$ and escape probability $P_{\mathrm{esc}}$. Lines: analytical calculations, where $P_S^{\mathrm{bound}}$ and $P_S^{\mathrm{pure}}$ are calculated via Eq. (1) ($j=0$ for $P_S^{\mathrm{pure}}$) for the experimental configuration shown in Fig. 2 and the parameters given in Appendix pp1 12. Shaded areas around $P_S^{\mathrm{bound}}$ and $P_{\mathrm{esc}}$ represent the uncertainties in the measured cavity parameters. Red dot with error bars: experimentally measured efficiency $P_S^{\exp }$; error bars are due to the uncertainty in the efficiency of detector and photon path. Dots: numerical simulations, taking into account our particular drive scheme introduced in Sec. 2. The numerically calculated efficiencies converge towards the analytic calculations for $\mathrm{\Omega }/\mathrm{\Delta }\ll 1$, where $\mathrm{\Omega }$ is the Rabi frequency of the drive laser and $\mathrm{\Delta }$ the common detuning of cavity and drive laser from the excited state. Slight deviations for higher $T_2$ are due to the finite evolution time used in the numerical simulations.

Figure 8

Possible efficiency improvements in our existing ion-cavity system. Theoretical predictions for $P_S^{\mathrm{bound}}$ and $P_S^{\mathrm{pure}}/P_S^{\mathrm{bound}}$, calculated via Eq. (1), with $j=0$ for $P_S^{\mathrm{pure}}$, when increasing the ion-cavity coupling strength $g$ over its current value $g_{\exp }$. Labels A–D represent possible schemes in our system. Theoretical predictions use mean values for experimental parameters. Scheme A corresponds to the current experimental configuration (Fig. 2), where $\zeta =\sqrt{0.5}$. Scheme B corresponds to changing the orientation of the drive beam and magnetic field axis to be parallel to the cavity axis, such that $\zeta =1$. Schemes C and D correspond to coupling two and three ions, respectively, in super-radiant entangled states to the cavity, in addition to scheme B. Red dot with error bars: measured efficiency for a drive field with $\mathrm{\Omega }=14$ MHz (Sec. 3). Horizontal gray line: photon escape probability through the cavity output mirror $P_{\mathrm{esc}}=T_2/(T_2+{\alpha }_{\mathrm{loss}})=0.78$.

Figure 9

Laser-pulse sequences for the experiments presented in the paper. An initialization laser pulse for intensity stabilization of the drive laser is followed by Doppler cooling. Subsequently, the ion is cooled close to the ground state of each of its three motional modes and prepared in the initial state $|u⟩=|S_{J=1/2},m_j=-1/2⟩$ via optical pumping ($10\mu \mathrm{s}$ of ${\sigma }^{-}$-polarized 397-nm light combined with 866 nm; 854 nm for repumping from the $D_{J=5/2}$ manifold). For the multiphoton experiment (Sec. 5) the drive-laser pulse, preceded by optical pumping, is repeated 15 times (“photontrain”). In the case of ion-photon entanglement (Sec. 4) the drive-laser pulse is bichromatic and ion-qubit rotations as well as ion-state detection are performed. See Fig. 6 for corresponding atomic transitions and Appendix pp7 for details on the lasers pulses for reconstructing the ion-photon entanglement.