Session X50: Quantum Information with Cold Atoms and Ions

Entanglement area law for long-range interacting systems

Area laws for entanglement provide crucial insight into the low-energy behavior of many-body systems and are intimately connected to the efficiency of classical computational methods. For 1D systems, an area law was rigorously proven for ground states of gapped Hamiltonians with local interactions and for states with exponentially decaying correlations. In the presence of long-range interactions, the proof of an area law for gapped ground states becomes much more challenging because long-range interactions can change the effective dimensionality of the system and introduce correlations decaying slower than an exponential. Based on recent theoretical advances that reveal strong remnants of locality in quenched systems with power-law decaying interactions, we prove an area law for a large class of gapped Hamiltonians with long-range interactions. As an intermediate step, we prove tight bounds on the decay of ground-state correlations.   

A System For High Flexibility Entangling Gates With Trapped Ions

Trapped ion qubits may be entangled via coupling to shared modes of motion using spin-dependent forces generated by optical fields. Residual qubit-motional coupling at the conclusion of the entangling operation is the dominant source of infidelity in this type of gate. For synchronously entangling increasing numbers of ions, longer gate times are required to minimise this residual coupling. We present a scheme that enables the state of each qubit to be simultaneously decoupled from all motional modes in an arbitrarily chosen gate time, increasing the gate fidelity and scalability. This is achieved by implementing discrete phase shifts in the optical field moderating the entangling operation. We describe an experimental system based on trapped ytterbium ions and demonstrate this scheme for two-qubit entangling gates on ytterbium ion pairs.   

Phase-modulated spin-motional decoupling with trapped ions

We present a technique to minimize residual spin-motional entanglement after a phonon-mediated entangling gate in trapped $^{171}\textrm{Yb}^{+}$ ion qubits. Phonon-mediated gates, such as the Mølmer-Sørensen gate, engineer spin-spin entanglement by coupling the qubits to their collective modes of motion. Consequently, a major experimental limitation is residual motional entanglement at the conclusion of the gate, resulting in a degradation of the final spin state purity. Our work utilizes phase-modulated pulse sequences to decouple the qubits from multiple motional modes simultaneously at a variable gate time. In addition, we extend this technique to the suppression of time-dependent noise using concatenated gate sequences, which allows for the recovery of a higher purity spin state. Using a single, experimentally controllable modulation parameter we are able to achieve more optimal quantum control in these gate sequences.   

The effect of electrode surface roughness on the motional heating rate of electromagnetic trapped ions

Electric field noise is a major source of motional heating in trapped ion quantum computation. While it is well known that this noise is influenced by trap electrode geometry in patch potential and surface adsorbate models, this has only been analyzed for smooth surfaces. We investigate the dependence of electric field noise on the roughness of surface electrodes by deriving a Green’s function describing this roughness, and evaluating its effects on adsorbate-surface binding energies. At cryogenic temperature, surface roughness is found to exponentially enhance or suppress heating rate, depending on the density distribution of surface adsorbates. Our result suggests that heating rates can be tuned over orders of magnitude by careful engineering of electrode surface profiles. \\ Reference\\ $[1]$ Q. Turchette, B. King, D. Leibfried, D. Meekhof, C. Myatt, M. Rowe, C. Sackett, C.Wood, W. Itano, C. Monroe, et al., Physical Review A 61, 063418 (2000).   

Universal critical phenomena of the cloud $\rightarrow$ crystal phase transition in the Paul trap: Powerlaws

$N$ charged particles, simultaneously stored in a radio-frequency (rf) Paul trap, exhibit deterministic heating. Depending on the damping ($\gamma$) imparted to the system, these particles can exist in multiple phases, the most commonly found being the cloud and crystal phases. With a small $\gamma$, the particles exhibit gas-like behavior, where the heating and cooling equilibrate and a stable cloud results. For larger $\gamma$, the damping overcomes the heating and the particles are forced into the crystalline state. We explore the cloud $\rightarrow$ crystal transition as a critical phenomenon. We find that the transition occurs at a critical value $\gamma_c$ of the damping constant $\gamma$. We find that as a function of $N$, $\gamma_c$ scales approximately like an iterated log law. We also present a universal power law, $\bar\tau_m \sim (\gamma - \gamma_c)^{-\beta}$, $\gamma > \gamma_c$, $\beta > 0$, independent of both $N$ and the Paul trap parameter $a$, depending only on the Paul trap parameter $q$, that describes the number of cycles necessary for the system to crystallize as a function of $\gamma-\gamma_c$.   

Ion-crystal metamorphoses in the Paul trap

We construct a generalized time-independent pseudo potential to describe the crystal morphologies and transitions between them for a three-ion Coulomb-interacting system in a Paul trap. The derivation of this pseudo potential extends a similar method that was already successfully constructed for the two-ion case to the case of three ions. Our method is based on keeping second-order micro-motion terms in the derivation of the pseudo potential. The resulting improved pseudo potential predicts ion-crystal morphologies that are corroborated by numerical simulations but are not captured by the standard pseudo potential. We provide a general method for extending this improved pseudo potential to a system of $N$ Coulomb-interacting ions in a Paul trap.   

Storage of multiple single-photon pulses emitted from a quantum dot in a solid-state quantum memory.

Quantum repeaters are critical components for distributing entanglement over long distances in presence of unavoidable optical losses during transmission. Stimulated by Duan-Lukin-Cirac-Zoller protocol, many improved quantum-repeater protocols based on quantum memories have been proposed, which commonly focus on the entanglement-distribution rate. Among these protocols, the elimination of multi-photons (multi-photon-pairs) and the use of multimode quantum memory are demonstrated to have the ability to greatly improve the entanglement-distribution rate. Here, we demonstrate the storage of deterministic single photons emitted from a quantum dot in a polarization-maintaining solid-state quantum memory; in addition, multi-temporal-mode memory with 1, 20 and 100 narrow single-photon pulses is also demonstrated. Multi-photons are eliminated, and only one photon at most is contained in each pulse. Moreover, the solid-state properties of both sub-systems make this configuration more stable and easier to be scalable. Our work will be helpful in the construction of efficient quantum repeaters based on all-solid-state devices.   

Towards the coupling of single photons from dye molecules to a photonic waveguide.

Single photons are very attractive for quantum information processing given their long coherence time and their ability to carry information in many degrees of freedom. A current challenge is the efficient generation of single photons in a photonic chip in order to scale up the complexity of quantum operations. We have proposed that a dibenzoterrylene (DBT) molecule inside an anthracene (AC) crystal could couple lifetime-limited indistinguishable single photons into a photonic waveguide if deposited in its vicinity. In this talk I describe the recent progress towards the realization of this proposal. A new method has been developed for evaporating AC and DBT to produce crystals that are wide and thin. The crystals are typically several microns across and have remarkably uniform thickness, which we control between 20 and 150 nm. The crystal growth is carried out in a glove bag in order to exclude oxygen, which improves the photostability of the DBT molecules by orders of magnitude. We image the fluorescence of single DBT molecules using confocal microscopy and analyse the polarization of this light to determine the alignment of the molecules. I will report on our efforts to control the alignement of the molecules by aligning the host matrix with the substrate.   

Ultra-Low Power Cross-Phase Shifts using Metastable Xenon in a High-Finesse Cavity

Many important applications in quantum information and quantum communications make use of weak single-photon nonlinearities. These nonlinearities have been produced using a number of methods, but they generally require a complicated experimental setup. We demonstrate a relatively simple system for producing ultra-low power cross-phase modulation, by using metastable xenon as the nonlinear medium within an optical cavity. Using metastable xenon prevents the degradation of optical surfaces which typically occurs with the use of alkali vapors such as rubidium. We produce phase shifts of up to 10 mrad using 4.5-fJ control pulses. We discuss the performance of this system and outline the planned improvements that will allow the cavity to produce single-photon phase shifts on the order of 1 mrad.   

Electric-Field Noise above a Thin Dielectric Layer on Metal Electrodes

The electric-field noise above a layered structure composed of a planar metal electrode covered by a thin dielectric is evaluated and it is found that the dielectric film considerably increases the noise level, in proportion to its thickness. Importantly, even a thin (mono) layer of a low-loss dielectric can enhance the noise level by several orders of magnitude compared to the noise above a bare metal. Close to this layered surface, the power spectral density of the electric field varies with the inverse fourth power of the distance to the surface, rather than with the inverse square, as it would above a bare metal surface. Furthermore, compared to a clean metal, where the noise spectrum does not vary with frequency (in the radio-wave and microwave bands), the dielectric layer can generate electric-field noise which scales in inverse proportion to the frequency. For various realistic scenarios, the noise levels predicted from this model are comparable to those observed in trapped-ion experiments. Thus, these findings are of particular importance for the understanding and mitigation of unwanted heating and decoherence in miniaturized ion traps.   

Carving complex many-atom entangled states by single-photon detection

We propose a versatile and efficient method to generate a broad class of complex entangled states of many atoms via the detection of a single photon. For an atomic ensemble contained in a strongly coupled optical cavity illuminated by weak single- or multi-frequency light, the atom-light interaction entangles the frequency spectrum of a transmitted photon with the collective spin of the atomic ensemble. Simple time-resolved detection of the transmitted photon then projects the atomic ensemble into a desired pure entangled state. This method can be implemented with existing technology, yields high success probability per trials, and can generate complex entangled states such as multicomponent Schr\"{o}dinger cat states with high fidelity.   

Exponentially small dependence of the Q-function on quantum coherence

We show that the Huisimi Q-function has an exponentially small dependence on the relative phase of a Schrodinger cat state, as might be expected from its definition. This raises the question as to whether or not the Q-function provides a complete description of the coherence of quantum states. We calculate the Q-function for a cat state and then invert it by first calculating the Glauber-Sudarshan P-function using a Fourier transform, which can then be used to calculate the state itself. This process is shown to multiply the small phase-dependent terms in the Q-function by an exponentially large factor as needed in order to obtain the original state once again. This exponential factor is strongly degraded by decoherence, such as by amplification of the original state.   

Generation and multi-pass propagation of a squeezed vacuum field in hot Rb vapor

We study a squeezed vacuum field (with reduced quantum noise level) generated in hot Rb vapor via the polarization self-rotation effect. By propagating the strong laser beam through a vapor cell once, we were able to achieve a noise suppression of 1.5-2 dB below shot noise. Our previous experiments showed that the amount of observed squeezing may be limited by the contamination of the squeezed vacuum output with higher-order spatial modes, also generated inside the cell. Here, we investigate whether or not the squeezing can be improved by making the light interact several times with a less dense atomic ensemble. We carry out a comparison of various conditions, e.g. injection power, atomic density, passing numbers etc., and studied their effect on squeezing level and the spatial structure of the output squeezed vacuum field. We believe(or show) optimization of the conditions can lead to higher achievable squeezing which would be very useful for precision metrology and quantum memory applications.   

Bright Single Photon Emitter in Silicon Carbide

Efficient, on-demand, and robust single photon emitters are of central importance to many areas of quantum information processing. Over the past 10 years, color centers in solids have emerged as excellent single photon emitters. Color centers in diamond are among the most intensively studied single photon emitters, but recently silicon carbide (SiC) has also been demonstrated to be an excellent host material. In contrast to diamond, SiC is a technologically important material that is widely used in optoelectronics, high power electronics, and microelectromechanical systems. It is commercially available in sizes up to 6 inches and processes for device engineering are well developed. We report on a visible-spectrum single photon emitter in 4H-SiC. The emitter is photostable at both room and low temperatures, and it enables 2 million photons/second from unpatterned bulk SiC. We observe two classes of orthogonally polarized emitters, each of which has parallel absorption and emission dipole orientations. Low temperature measurements reveal a narrow zero phonon line with linewidth $<$ 0.1~nm that accounts for more than 30\% of the total photoluminescence spectrum. To our knowledge, this SiC color emitter is the brightest stable room-temperature single photon emitter ever observed.   

Ring-shaped Wigner crystals of trapped ions at the micronscale

Trapped ion crystals are ideal platforms to study many-body physics and quantum information processing, with both the internal electronic states and external motional degree-of-freedoms controllable at the single quantum level. In contrast to conventional, finite, linear chains of ions, a ring topology exhibiting periodic boundary conditions and rotational symmetry opens up a new directions to diverse topics. However, previous implementations of ion rings result in small aspect ratios (\textless 0.07) of ion-electrode distance to ring diameter, making the rotational symmetry of the ion crystals prone to stray electric fields from imperfections of the trap electrodes, particularly evident at low temperatures. Here, using a new trap design with a 60-fold improvement of this aspect ratio, we demonstrate crystallization of $^{\mathrm{40}}$Ca$^{\mathrm{+}}$ ions in a ring with rotational energy barriers comparable to the thermal energy of Doppler laser cooled ion crystals. When further reducing the rotational energy barriers, we observe delocalization of the ion rings. With this result, we enter a regime where quantum topological effects can be studied and novel quantum computation and simulation experiments can be implemented.