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A single-photon switch and transistor enabled by a solid-state quantum memory

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Science  06 Jul 2018:
Vol. 361, Issue 6397, pp. 57-60
DOI: 10.1126/science.aat3581

A single-photon gate

A long-standing goal in optics is to produce a solid-state alloptical transistor, in which the transmission of light can be controlled by a single photon that acts as a gate or switch. Sun et al. used a solid-state system comprising a quantum dot embedded in a photonic crystal cavity to show that transmission through the cavity can be controlled with a single photon. The single photon is used to manipulate the occupation of electronic energy levels within the quantum dot, which in turn changes its optical properties. With the gate open, about 28 photons can get through the cavity on average, thus demonstrating single-photon switching and the gain for an optical transistor.

Science, this issue p. 57

Abstract

Single-photon switches and transistors generate strong photon-photon interactions that are essential for quantum circuits and networks. However, the deterministic control of an optical signal with a single photon requires strong interactions with a quantum memory, which has been challenging to achieve in a solid-state platform. We demonstrate a single-photon switch and transistor enabled by a solid-state quantum memory. Our device consists of a semiconductor spin qubit strongly coupled to a nanophotonic cavity. The spin qubit enables a single 63-picosecond gate photon to switch a signal field containing up to an average of 27.7 photons before the internal state of the device resets. Our results show that semiconductor nanophotonic devices can produce strong and controlled photon-photon interactions that could enable high-bandwidth photonic quantum information processing.

Photons are ideal carriers of quantum information, but the lack of deterministic photon-photon interactions has limited their applications in quantum computation and quantum networking. Recent advances in strong light-matter interactions using neutral trapped atoms (15) have enabled optical nonlinearities operating at the fundamental single-photon regime. However, neutral atoms require large and complex laser traps and operate at low bandwidths on the order of megahertz, which makes it challenging to integrate into compact devices. Circuit quantum electrodynamics systems also support strong nonlinearities (6, 7), but they operate only in the microwave regime and are difficult to scale to optical frequencies. The realization of a compact solid-state single-photon nonlinearity at optical frequencies remains a key missing ingredient for scalable chip-integrated quantum photonic circuits.

Nanophotonic structures coupled to quantum emitters offer an attractive approach to realize single-photon nonlinearities in a compact solid-state device. However, most previous works used quantum emitters that act as two-level atomic systems (8), which are fundamentally limited by a time-bandwidth trade-off that makes deterministic single-photon switching impossible in either waveguides (9, 10) or cavities (11, 12). A quantum memory can overcome this limit, enabling a single photon to deterministically switch a second photon (13). It can also realize a single-photon transistor where one photon switches a signal containing multiple photons (14), a crucial building block for scalable quantum circuits (15). Recently, there has been great progress in controlling photons with solid-state qubits (16, 17), as well as controlling a solid-state qubit with a photon (18). However, neither a single-photon switch nor a single-photon transistor has been realized using a solid-state quantum memory.

We report a single-photon switch and transistor enabled by a solid-state spin qubit coupled to a nanocavity. Our spin qubit comprises a single electron in a charged quantum dot. The quantum dot energy level structure (Fig. 1A) includes two ground states with opposite electron spin that form a stable quantum memory, labeled as Embedded Image and Embedded Image, and two excited states that contain a pair of electrons and a single hole with opposite spins, labeled as Embedded Image and Embedded Image. We apply a magnetic field in the Voigt configuration to break the spin degeneracy. In this condition, all four transitions are optically allowed, but the polarization of transitions σ1 and σ4 is orthogonal with transitions σ2 and σ3. Figure 1B shows a scanning electron microscope image of the fabricated cavity, which is based on a three-hole defect in a two-dimensional photonic crystal (19). The cavity mode is linearly polarized and makes a 30° angle with the polarization of transition σ1 (19). We attain spin-dependent coupling by applying a magnetic field of 5.5 T. At this magnetic field, transition σ1 is resonant with the cavity while all other transitions are detuned. Using cross-polarized reflectivity measurements, we determine the coupling strength g, cavity energy decay rate κ, and transition σ1 dipole decoherence rate γ to be g/2π = 10.7 ± 0.2 GHz, κ/2π = 35.5 ± 0.6 GHz, and γ/2π = 3.5 ± 0.3 GHz, respectively (19).

Fig. 1 Schematics of a single-photon switch and transistor.

(A) Energy-level structure of a charged quantum dot in the Voigt configuration. The quantum dot has four optical transitions labeled as σ1 to σ4. Only transition σ1 resonantly couples to the optical cavity. (B) Scanning electron microscope image of a fabricated photonic crystal cavity. (C) Schematic of the working principle of the single-photon switch and transistor. In the first step, a gate photon controls the state of the spin. In the second step, the spin determines the polarization of the signal field. (D) Pulse timing diagram to implement the single-photon switch and transistor.

In the working principle of the single-photon switch and transistor (Fig. 1C), a gate pulse first sets the internal quantum memory of the switch. If the gate pulse contains zero photons, the spin stays in the spin-down state. But if the gate pulse contains one photon, it sets the spin to spin-up. Subsequently, the spin-state controls the cavity reflection coefficient, thereby changing the polarization of reflected signal photons. Figure 1D shows the pulse sequence to implement these two steps. We first prepare the quantum dot in a superposition of its spin ground states given by Embedded Image using an initialization pulse to optically pump the spin to spin-down, followed by a circularly polarized optical rotation pulse that creates a π/2 spin rotation through cavity leaky modes (20, 21). The system then freely evolves for a time τ, followed by a second identical rotation pulse. We inject the gate pulse between these two spin rotation pulses. If we set the free evolution time to be an integer number plus one-half of spin precession period, then in the absence of a gate photon the spin will evolve to the state Embedded Image and the second rotation pulse will rotate it back to the spin-down state. But if a single gate photon reflects from the cavity, it applies a relative π phase shift between the spin-up and spin-down state, which reflects the spin along the x axis of the Bloch sphere. In this case the second rotation pulse rotates the spin to the spin-up state. A circularly polarized signal field then reflects off the cavity and undergoes a spin-dependent polarization rotation (19).

We prepare the pulse sequence in Fig. 1D using a pair of synchronized mode-locked lasers and an amplitude-modulated external cavity laser diode (19). We first characterize the switching behavior of the device using a signal field that has an average of 13.3 photons per pulse after the objective lens, corresponding to Ns = 0.42 ± 0.05 photons per pulse contained within the transverse spatial mode of the cavity. We determine the coupling efficiency (3.16 ± 0.35%) using the back-action of the input photons on the spin (19). We also measure the average power of each π/2-rotation pulse to be 20 μW after the objective lens. We prepare the incident signal field in the right-circular polarization and measure the intensity of the left-circular polarization component of the reflected signal field using a fixed polarizer after the cavity. Figure 2A shows the measured transmittance of the signal field passing through the polarizer as a function of τ in the absence of the gate pulse. We define the transmittance contrast as δ = TupTdown, where Tup and Tdown are the transmittance of the signal field when the rotation pulses prepare the spin to spin-up and spin-down, respectively, corresponding to the maximum and minimum transmittance in the oscillation. From the numerical fit (solid line) (19), we calculate the transmittance contrast to be δ = 0.24 ± 0.01. This value differs from the ideal contrast of unity due to both imperfect spin preparation fidelity of F = 0.78 ± 0.01 after the two rotation pulses and a finite cooperativity of C = 2g2/κγ = 1.96 ± 0.19.

Fig. 2 Demonstration of a single-photon switch and transistor.

(A) Transmittance of the signal field in the absence of the gate field as a function of delay time τ between two spin rotation pulses. (B) Transmittance of the signal field conditioned on detecting a gate photon as a function of delay time τ between the two spin rotation pulses. (C) Conditional transmittance of the signal field as a function of delay time τ between the two spin rotation pulses with (blue) and without (orange) a gate photon when we set the average signal photon number per pulse to be 4.4 ± 0.5, 10.9 ± 1.2, and 23.0 ± 2.5, respectively. In all panels, the orange squares and blue circles show measured transmittance without the gate field and conditioned on detecting a gate photon, respectively. The solid lines show numerically calculated values. The vertical solid line (a) and dashed line (b) denote the two optimal operating conditions of the single-photon switch and transistor.

We next inject a 63-ps gate pulse containing an average of 13.3 photons after the objective lens, corresponding to 0.21 photons per pulse coupled to the cavity. We prepare the gate field in the same circular polarization as the signal, and post-select those events where the gate photon couples to the cavity using a two-photon coincidence measurement between the reflected gate and signal photons (19). Figure 2B shows the transmittance of the signal field conditioned on the presence of an incident gate photon that couples to the cavity. The oscillations of the transmittance shift by π due to spin-flips induced by a single gate photon.

The vertical solid line (labeled as a in Fig. 2) indicates the condition where the spin undergoes an integer number of rotations plus one half rotation around the Bloch sphere during its free evolution time. At this condition, a gate photon causes the polarization of the signal field to rotate and preferentially transmit through the polarizer, as described in Fig. 1C. The vertical dashed line b shows a second operating condition that also leads to optimal switching operation. This condition corresponds to the reverse switching behavior where the gate photon prevents the signal field polarization from rotating, thereby decreasing the transmittance. At both conditions, the gate pulse induces a change in the signal transmittance by 0.21 ± 0.02. For an ideal gate pulse containing a single photon, the transmittance change should be equal to the transmittance contrast of 0.24 calculated in Fig. 2A. In our case, the change in transmittance is slightly degraded because we use an attenuated laser to produce the gate pulse, which has a small probability of containing multiple photons. We define the switching contrast ξ as the change in the transmittance induced by a single gate photon. By correcting for multiphoton events in the gate field (19), we attain ξ = 0.24 ± 0.02, which matches the transmittance contrast δ.

The quantum memory in our device has a lifetime that is appreciably longer than the bandwidth of the switch. Thus, once a gate photon sets the memory state, the device can switch many signal photons before the spin-state decays. This property enables a single-photon transistor where a single gate photon can control a signal composed of many photons, an important distinction from switches lacking a quantum memory (912). Figure 2C shows the transmittance of the signal field as a function of delay time τ, where the average number of signal photons Ns per pulse is set to be 4.4 ± 0.5, 10.9 ± 1.2, and 23.0 ± 2.5, respectively. Here, we fixed the signal pulse to be 1.34 ns long, which is much longer than device bandwidth (1/2g = 7 ps) but much shorter than the spin T1 time (microseconds to milliseconds) (22). These conditions guarantee that the switching contrast depends only on the signal photon number as long as we are in the weak excitation regime (Ns << 115). The transmittance shows clear switching behavior for all cases. We calculate the switching contrast at the three signal photon numbers to be ξ = 0.22 ± 0.03, ξ = 0.17 ± 0.02, and ξ = 0.12 ± 0.02, respectively.

The switching contrast degrades with increasing signal photon number because each signal photon can apply a weak back-action on the spin through inelastic Raman scattering, inducing an undesired spin-flip that resets the internal quantum memory. This weak back-action limits the number of signal photons that can reflect from the cavity before a spin-flip event resets the spin-state. It therefore limits many applications. For example, in nondestructive single-photon detection, the maximum number of signal photons sets the overall detection efficiency. The blue circles in Fig. 3A show the measured transmittance contrast in the absence of the gate pulse as a function of the average signal photon number. This contrast quantifies the degree of self-switching induced by the signal without a gate field. The solid line shows a numerical fit of the data to an exponential function of the form exp(–Ns/Navg), where Navg is the average number of signal photons it takes to flip the spin. From the fit, we determine Navg = 27.7 ± 8.3.

Fig. 3 Gain of the single-photon transistor.

(A) Transmittance contrast as a function of average signal photon number. (B) Transistor gain as a function of average signal photon number. In both panels, blue circles show the measured values, and blue solid lines show the numerical fits.

An important feature of transistors is that they exhibit a gain above unity. We define the gain as the change in the average number of transmitted signal photons induced by a single gate photon (13). We determine the gain using the difference in the number of transmitted signal photons averaged over many pulse cycles when the spin is coherently prepared in spin-up and spin-down states, respectively, given by G = Nsδ. The gain increases initially with the signal photon number (Fig. 3B) but saturates at strong signal fields and tapers down due to an increased probability of spin-flip from inelastic scattering and deviations from the weak excitation regime. We achieve the maximum gain of G = 3.3 ± 0.4 with a photon number of Ns = 29.2 ± 3.2.

The switching contrast and gain of our current device is limited by the spin preparation fidelity and finite cooperativity. The spin preparation fidelity could be improved by incorporating actively charged device structures (21). Electric gating could also reduce spectral wandering to enable much larger cooperativities (23). Higher-Q cavities and better alignment of the cavity polarization could create a larger selective Purcell enhancement for transition σ1 that would reduce Raman scattering and therefore increase the device gain. Currently, we excite and collect from the out-of-plane direction, which results in low coupling and collection efficiency that limits the usable gain. A scalable device suitable for quantum information processing will require much higher efficiencies, because photon loss constitutes a dominant error mechanism for photonic qubits. Recent progress has been made in improving coupling efficiency of nanophotonic devices, including using adiabatic tapered structures to directly couple to fiber (24), adopting designs that have better spatial mode-matching with a fiber (25), or by coupling directly to on-chip waveguides (26). On-chip tuning (27) or hybrid integration (28, 29) could further enable integration of multiple qubits and cascaded devices. Ultimately, such a device could enable a variety of important applications using compact chip-integrated platforms, including low-energy electro-optics (30), photonic quantum circuits (15), nondestructive photon detection (31), and scalable quantum repeaters for quantum networks (32).

Supplementary Materials

www.sciencemag.org/content/361/6397/57/suppl/DC1

Materials and Methods

Supplementary Text

Figs. S1 to S7

References (3344)

References and Notes

  1. Materials and methods are available as supplementary materials.
Acknowledgments: The authors acknowledge G. Baumgartner and M. Morris at the Laboratory for Telecommunication Sciences for providing superconducting nanowire single-photon detectors. Funding: This work was supported by the Physics Frontier Center at the Joint Quantum Institute, the National Science Foundation (grants PHY1415485 and ECCS1508897), and the ARL Center for Distributed Quantum Information. Author contributions: S.S. and E.W. conceived and designed the experiment, prepared the manuscript, and carried out the theoretical analysis. S.S. carried out the measurement and analyzed the data. H.K. contributed to sample fabrication. Z.L. contributed to optical measurement. G.S.S. provided samples grown by molecular beam epitaxy. Competing interests: The authors declare no competing financial interests. Data and materials availability: All data are available in the manuscript or the supplementary materials.
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