Session V45: Semiconductor Qubits: Optical and Microwave Control

Generation of heralded entanglement between distant quantum dot hole spins

Entanglement plays a central role in fundamental tests of quantum mechanics as well as in the burgeoning field of quantum information processing. Particularly in the context of quantum networks and communication, some of the major challenges are the efficient generation of entanglement between stationary (spin) and propagating (photon) qubits, the transfer of information from flying to stationary qubits, and the efficient generation of entanglement between distant stationary (spin) qubits. In this talk, I will present such experimental implementations achieved in our team with semiconductor self-assembled quantum dots.\\ \\Not only are self-assembled quantum dots good single-photon emitters, but they can host an electron or a hole whose spin serves as a quantum memory, and then present spin-dependent optical selection rules leading to an efficient spin-photon quantum interface. Moreover InGaAs quantum dots grown on GaAs substrate can profit from the maturity of III-V semiconductor technology and can be embedded in semiconductor structures like photonic cavities and Schottky diodes.\\ \\I will report on the realization of heralded quantum entanglement between two semiconductor quantum dot hole spins separated by more than five meters. The entanglement generation scheme relies on single photon interference of Raman scattered light from both dots. A single photon detection projects the system into a maximally entangled state. We developed a delayed two-photon interference scheme that allows for efficient verification of quantum correlations. Moreover the efficient spin-photon interface provided by self-assembled quantum dots allows us to reach an unprecedented rate of 2300 entangled spin pairs per second, which represents an improvement of four orders of magnitude as compared to prior experiments carried out in other systems.\\ \\Our results extend previous demonstrations in single trapped ions or neutral atoms, in atom ensembles and nitrogen vacancy centers to the domain of artificial atoms in semiconductor nanostructures that allow for on-chip integration of electronic and photonic elements. This work lays the groundwork for the realization of quantum repeaters and quantum networks on a chip.   

Polarisation singularities in disordered photonic crystal waveguides for on-chip spin-photon entanglement.

A polarisation singularity occurs at a position in a vector field where one of the parameters of the local polarisation ellipse (handedness, eccentricity or orientation) becomes singular. With the vector nature of electromagnetic fields, optics is an obvious place for the study of polarisation singularities, and they can be found in systems ranging from tightly focused beams to speckle fields. Here we demonstrate that photonic crystal waveguides support on-chip polarisation singularities. As Bloch waves, the eigenmodes of photonic crystal waveguides possess a strong longitudinal, as well as transverse, component of their electric field. The spatial dependence of both these components and the phase between them ensures a rich and complex polarisation landscape in the waveguide. Recently, the use of polarisation singularities found in photonic crystal waveguides is generating much interest for integrated quantum information applications, as they can couple the spin-states of electrons confined to quantum dots to the optical modes of the waveguide. For example, at a circular-point (C-point), the sign of the local helicity is governed by the propagation direction of the optical mode, which allows for spin-photon coupling to one direction only. However, any real system will inevitably contain imperfections, and it is not obvious that the polarisation singularities will persist in the disordered waveguides. Here, we use calculations of the eigenmodes of disordered waveguides to demonstrate that the polarisation singularities persist far beyond realistically expected levels of disorder.   

Optical control of Berry phase in a diamond spin qubit

Geometric phase, a fascinating quantum mechanical phenomenon that arises from cyclic state evolution, is a promising avenue to realize fault-tolerant quantum information processing. Here, we demonstrate an all-optical approach to accumulate a geometric phase, or Berry phase, within a solid-state spin qubit, the nitrogen-vacancy center in diamond \footnote{C. G. Yale*, F. J. Heremans*, B. B. Zhou,* A. Auer, G. Burkard, D. D. Awschalom, arXiv:1507.08993 (2015).}. With stimulated Raman adiabatic passage (STIRAP), we evolve two light fields to cycle the resulting dark state of a low temperature lambda system in a `tangerine slice' trajectory that we examine through time-resolved state tomography. This type of trajectory acquires a Berry phase which we then measure through phase comparison to a reference state. We then probe the limits of this control as a result of adiabatic breakdown for short timescales and unintended excitation driven by far-detuned optical fields that accumulate for long timescales. We also investigate the intrinsic resilience of this Berry phase to noise introduced into the system, which is the focus of the following talk. As an all-optical approach, this geometric control represents a pathway to the development of optical geometric gates in the solid state.   

Robustness of optically-controlled Berry phase in a diamond spin qubit

The intrinsic noise resilience of geometric phases has motivated their application as an alternative protocol for realizing high fidelity quantum operations. Using stimulated Raman adiabatic passage (STIRAP) to cyclically evolve the dark state of a lambda system, we demonstrate all-optical control over Berry phase for a single spin in the solid state, the nitrogen vacancy center in diamond [1]. Here we introduce both phase and amplitude noise into the optical control fields for a class of `tangerine slice' trajectories on the Bloch sphere. We examine the response of Berry phase to scaling of the noise amplitude and adiabatic cycle time, finding Berry phase to be unaffected by deviations parallel to the trajectory and to increase in robustness for long cycle times. Moreover, our noise resilience is independent of the value of the accumulated Berry phase, a property that differs from the behavior of circular trajectories investigated by prior microwave techniques. We also discuss potential improvements to our work. \\[4pt] [1] C. G. Yale*, F. J. Heremans*, B. B. Zhou,* A. Auer, G. Burkard, D. D. Awschalom, arXiv:1507.08993 (2015).   

Quantum nanophotonics: Controlling a photon with a single spin

The implementation of quantum network and distributive quantum computation replies on strong interactions between stationary matter qubits and flying photons. The spin of a single electron confined in a quantum dot is considered as a promising matter qubit as it possesses microsecond coherence time and allows picosecond timescale control using optical pulses. The quantum dot spin can also interact with a photon by controlling the optical response of a strongly coupled cavity. In this talk I will discuss our recent work on an experimental realization of a spin-photon quantum phase switch using a single spin in a quantum dot strongly coupled to a photonic crystal cavity. We show large modulation of the cavity reflection spectrum by manipulating the spin states of the quantum dot, which enables us to control the quantum state of a reflected photon. We also show the complementary effect where the presence of a single photon switches the quantum state of the spin. The reported spin-photon quantum phase operation can switch spin or photon states in picoseconds timescale, representing an important step towards GHz semiconductor based quantum logic devices on-a-chip and solid-state implementations of quantum networks.   

A quantum phase switch between a solid state spin and a photon

The implementation of quantum network and distributive quantum computation replies on strong interactions between stationary matter qubits and flying photons. The spin of a single electron confined in a quantum dot is considered as a promising matter qubit as it possesses microsecond coherence time and allows picosecond timescale control using optical pulses. The quantum dot spin can also interact with a photon by controlling the optical response of a strongly coupled cavity. In this talk I will discuss our recent work on an experimental realization of a spin-photon quantum phase switch using a single spin in a quantum dot strongly coupled to a photonic crystal cavity. We show large modulation of the cavity reflection spectrum by manipulating the spin states of the quantum dot, which enables us to control the quantum state of a reflected photon. We also show the complementary effect where the presence of a single photon switches the quantum state of the spin. The reported spin-photon quantum phase operation can switch spin or photon states in picoseconds timescale, representing an important step towards GHz semiconductor based quantum logic devices on-a-chip and solid-state implementations of quantum networks.   

Efficient generation of indistinguishable single photons on-demand at telecom wavelengths

Highly efficient single photon sources are important building blocks for optical quantum information processing. For practical use and long-distance quantum communication, single photons should have fiber-compatible telecom wavelengths. In addition, most quantum communication applications require high degree of indistinguishability of single photons, such that they exhibit interference on a beam splitter. However, deterministic generation of indistinguishable single photons with high brightness remains a challenging problem in particular at telecom wavelengths. We demonstrate a telecom wavelength source of indistinguishable single photons using an InAs/InP quantum dot in a nanophotonic cavity. To obtain the efficient single quantum dot emission, we employ the higher order mode in L3 photonic crystal cavity that shows a nearly Gaussian transverse mode profile and results in out-coupling efficiency exceeding 46 {\%} and unusual bright single quantum dot emission exceeding 1.5 million counts per second at a detector. We also observe Purcell enhanced spontaneous emission rate as large as 4 and high linear polarization ratio of 0.96 for the coupled dots. Using this source, we generate high purity single photons at 1.3 $\mu $m wavelength and demonstrate the indistinguishable nature of the emission using a two-photon interference measurement.   

Quantum Dot Device Design Optimization for Resonator Coupling

Coupling a semiconductor quantum dot qubit to a superconducting resonator broadens the possibilities for interqubit communication and potentially allows integration of quantum dots with other qubit systems. The major technological hurdle that must be overcome is reaching the strong coupling limit, where the coupling frequency between the resonator and the qubit is larger than both the qubit decoherence rate and the photon loss rate of the resonator. In this work, we examine optimization of the quantum dot device design. Using the Thomas-Fermi approximation in conjunction with a metallic dot capacitive model, we focus on improving the capacitive coupling between a resonator gate and a quantum dot while decreasing the cross-coupling to nearby dots. Through these simulations, we find that the optimization follows an intuitive geometric relation.   

A Dressed Spin Qubit in Silicon

Coherent dressing of a quantum two-level system has been demonstrated on a variety of systems, including atoms, self-assembled quantum dots, and superconducting quantum bits, and can be demonstrated by measuring Rabi oscillations, or a Mollow triplet in the spectrum. It can be used to gain access to a new quantum system with improved properties - a different and tunable level splitting, faster and easier control, and longer coherence times. In our work we investigate the properties of the dressed, donor-bound electron spin in silicon, and probe its potential for the use as quantum bit in scalable architectures. Here, the two dressed spin-polariton levels constitute the quantum bit. The dressed qubit can be coherently driven with an oscillating magnetic field, an oscillating electric field, by frequency modulating the driving field, or by a simple detuning pulse. We measure coherence times of T2* $=$ 2.4 ms and T2 $=$ 9 ms (Hahn echo), one order of magnitude longer than those of the undressed qubit.   

Gate sensing coherent charge oscillations in a silicon field-effect transistor.

We report the observation of coherent charge oscillations in a double quantum dot formed in a silicon nanowire transistor detected via its dispersive interaction with a radio-frequency resonant circuit coupled via the gate. Differential capacitance changes at the inter-dot charge transitions allow us to monitor the state of the system in the strong-driving regime where we observe the emergence of Landau-Zener-St\"{u}ckelberg-Majorana interference on the phase response of the resonator. A theoretical analysis of the dispersive signal demonstrates that quantum and tunnelling capacitance changes must be included to describe the qubit-resonator interaction. Furthermore, a Fourier analysis of the interference pattern reveals a charge coherence time, T$_{\mathrm{2}}=$ 100 ps. Our results demonstrate charge coherent control and readout in a simple silicon transistor and open up the possibility to implement charge and spin qubits in existing complementary metal-oxide-semiconductor technology.   

Coplanar photonic bandgap resonators for low temperature electron and nuclear magnetic resonance spectroscopy

In recent years, superconducting coplanar waveguide (CPW) resonators have become a useful tool for low temperature pulsed electron spin resonance (ESR), even at dilution refrigerator temperatures. Their small mode volumes make CPW resonators particularly well suited to measuring small numbers of spins near the resonator surface, since in this region the spin sensitivity is very high. While these resonators have proven useful for ESR at single microwave frequencies, it is difficult to also manipulate nuclear spins in electron-nuclear-double resonance (ENDOR) experiments, since manipulation of nuclear spins requires radio frequency (RF) magnetic fields. Ideally one would simply generate these fields by passing RF currents through the CPW, but because conventional CPW resonators are capacitively coupled, they will not transmit low-frequency RF currents. In this talk, we discuss the use of one dimensional photonic bandgap (PBG) resonators to overcome this challenge. PBG resonators are a promising alternative to conventional CPW resonators since they offer high quality factors at microwave frequencies, while simultaneously allowing transmission of nonresonant RF currents below the photonic bandgap. Here, we will discuss PBG resonator designs and present data showing their use for low temperature ESR of donors in $^{\mathrm{28}}$Si. Initial ENDOR results will also be presented.   

Theory of nuclear spin dephasing and relaxation by optically illuminated nitrogen vacancy center.

Dephasing and relaxation of the nuclear spins coupled to the nitrogen-vacancy (NV) center during optical initialization and readout is an important issue for various applications of this hybrid quantum register. Here we present both an analytical description and a numerical simulation for this process, which agree reasonably with the experimental measurements. For the NV center under cyclic optical transition, our analytical formulas not only provide a clear physics picture, but also allows controlling the nuclear spin dissipation by tuning an external magnetic field. For more general optical pumping, our analytical formulas reveal significant contribution to the nuclear spin dissipation due to electron random hopping into/out of the $m=0$ (or $m=\pm1$) subspace. This contribution is not suppressed even under saturated optical pumping and/or vanishing magnetic field, thus providing a possible solution to the puzzling observation of nuclear spin dephasing in zero perpendicular magnetic field [M. V. G. Dutt \textit{et al}., Science \textbf{316}, 1312 (2007)]. It also implies that enhancing the degree of spin polarization of the nitrogen-vacancy center can reduce the effect of optical induced nuclear spin dissipation.