Quantum-Logic Gate between Two Optical Photons with an Average Efficiency above 40%

Optical qubits uniquely combine information transfer in optical fibers with a good processing capability and are therefore attractive tools for quantum technologies. A large challenge, however, is to overcome the low efficiency of two-qubit logic gates. The experimentally achieved efficiency in an optical controlled not (cnot) gate reached approximately 11% in 2003 and has seen no increase since. Here, we report on a new platform that was designed to surpass this long-standing record. The new scheme avoids inherently probabilistic protocols and, instead, combines aspects of two established quantum nonlinear systems: atom-cavity systems and Rydberg electromagnetically induced transparency. We demonstrate a cnot gate between two optical photons with an average efficiency of 41.7(5)% at a postselected process fidelity of 81(2)%. Moreover, we extend the scheme to a cnot gate with multiple target qubits and produce entangled states of presently up to five photons. All these achievements are promising and have the potential to advance optical quantum information processing in which almost all advanced protocols would profit from high-efficiency logic gates.

Popular Summary

Optical quantum information processing has been tremendously successful, but further progress in the field is hampered by the low efficiency of the two-qubit quantum gates realized so far. These gates take two photons as input and then, after some manipulation, transmit both; low efficiency means a low probability that both photons are transmitted. Despite major efforts, the record of the experimentally achieved efficiency, approximately 11%, has not improved in the past 20 years. We now demonstrate an optical two-qubit gate with an average efficiency above 40%, thus outperforming the previous record by a factor of almost 4.

This breakthrough is based on a new experimental platform, in which an ultracold gas of a few hundred atoms is positioned inside an optical resonator. Two photons enter the setup and then depart with their polarizations altered by atomic interactions in the cavity. This implements a controlled not gate.

We accomplish this with a process called electromagnetically induced transparency. Incoming photons are converted into polaritons, quasiparticles consisting of a photon tightly coupled to a propagating, highly excited atomic state known as a Rydberg state. Any two atoms in such a state have a strong interaction, even at large separations. When two photons enter our resonator, both become polaritons and their Rydberg components interact. When the excitations leave the gas, they become just photons, but ones whose phase has been changed by the Rydberg interaction. A dual-rail scheme converts this change in phase into a change in polarization.

Theoretical study suggests that even higher efficiency can be expected in the present platform with further technical improvements. This work opens many new possibilities in optical quantum information processing, in which almost all advanced protocols could profit from high-efficiency gates.

Figure 1

(a) Scheme of the gate. The control (target) photon pulse travels through the setup from left to right (right to left). Polarizing beam splitters (PBSs, blue squares) map between incoming and outgoing polarization qubits and internal dual-rail qubits. One rail of each qubit impinges on the cavity, and the other rail bypasses the cavity. If the control qubit impinges on the cavity, it is stored in a Rydberg state. Subsequently, the target photon enters the system. A conditional $\pi$ phase shift is experienced if both qubits are in their cavity rails. After the interaction with the target photon, the control photon is retrieved. The bypass rail of the control qubit is delayed in an optical fiber to match the delay resulting from storage. The octagon represents the vacuum chamber. (b) Atomic level scheme. Coupling light (blue, cyan) creates EIT for the signal light (red, purple). (c) Timing sequence of the light power of the incoming pulses. The vertical axis uses different scales for different light fields. In the first microsecond, the control pulse is stored; in the second microsecond, the target pulse interacts with the system; and in the third microsecond, the control pulse is retrieved.

Figure 2

Truth tables and Bell-state tomography. (a) Postselected truth table in the CPHASE basis. The average fidelity is 99.4(4)%. All error bars in this paper represent a statistical uncertainty of 1 standard deviation. (b) Postselected truth table in a cnot basis. The average fidelity is 87(1)%. (c,d) Real and imaginary parts of the reconstructed postselected density matrix obtained in an entangling gate operation. The postselected Bell-state fidelity is 79(2)%.

Figure 3

Quantum process tomography. Real and imaginary parts of the elements of the postselected $16\times 16$ process matrix ${\chi }^{\mathrm{ps}}$. The basis for the matrix representation is chosen such that for the ideal gate, one matrix element would equal unity and all others would vanish. The postselected process fidelity is 81(2)%.

Figure 4

Multiphoton entanglement. To verify genuine $N$-photon entanglement, we study parity oscillations. To this end, we measure all photons in the same polarization basis $(|b_{\vartheta ,+}⟩,|b_{\vartheta ,-}⟩)$ with $|b_{\vartheta ,\pm }⟩=(|H⟩\pm e^{i\vartheta }|V⟩)/\sqrt{2}$, where $\vartheta$ is real. The measurement outcomes yield the generalized Stokes parameter $S_{\vartheta }^{(N)}=⟨M_{\vartheta }^{\otimes N}⟩$, where $M_{\vartheta }=|b_{\vartheta ,+}⟩⟨b_{\vartheta ,+}|-|b_{\vartheta ,-}⟩⟨b_{\vartheta ,-}|$ is the single-qubit operator describing the projection of the Stokes vector along a suitable direction. The dots show measured values of $S_{\vartheta }^{(N)}$ as a function of $\vartheta$ for (a) $N=3$, (b) $N=4$, (c) $N=5$, and (d) $N=6$. The lines are fits; see Appendix pp5.

Figure 5

(a) The real part $\mathrm{Re}({\xi }^{\mathrm{ps}})$ of the measured postselected reduced process matrix contains all the dominant experimental imperfections of the gate. (b) A model accounting for two single-qubit visibilities, which are used as free fit parameters, and for the fixed known efficiencies, agrees well with the experimental data in (a).

Figure 6

The populations $p_H$, $p_V$, and ${\mathcal{P}}_N$ and the coherence ${\mathcal{C}}_N$ of the observed GHZ states depend on the number of detected photons, $N$. The lines show results from a simple model, which contains only one free fit parameter $V_c$. This parameter affects only ${\mathcal{C}}_N$. The model agrees fairly well with the data. According to the model, the nonideal visibilities are the dominant experimental imperfections.

Figure 7

Cavity Rydberg EIT spectra. (a) Relative intensity and (b) phase of the light reflected from the cavity shown as a function of the signal detuning ${\mathrm{\Delta }}_c/2\pi$. Red (blue) data were recorded in the absence (presence) of EIT coupling light. The experiment is well within in the regime of large normal-mode splitting. The blue data clearly show an EIT feature at zero detuning. Fits (lines) to the data (dots) reveal important experimental parameters, namely, the collective cooperativity $C$, the EIT coupling Rabi frequency $\mathrm{\Omega }$, and the coherence time $1/{\gamma }_{rg}$.

Figure 8

Geometry of the bow-tie cavity. Two of the beams inside the cavity are parallel. These beams have lengths of $L_1=30.75\mathrm{mm}$ and $L_2=63.00\mathrm{mm}$. The angle of incidence is 4.5°. The two mirrors separated by the shorter distance $L_1$ are concave with radii of curvature of $-25\mathrm{mm}$. The cavity waist $w_c=8.5\mu \mathrm{m}$ and the atomic ensemble are located midway between these two mirrors. The other two mirrors are convex with radii of curvature of 50 mm. One of the convex mirrors serves as the input-output coupler for signal light. The substrate of each concave (convex) mirror has a diameter of 6.35 mm (7.75 mm).