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Conference on Lasers and Electro-Optics

Quantum simulation with N=19 Rydberg atoms for quantum Ising dynamics

Hyosub Kim, Kyungtae Kim, Woojun Lee, Jaewook Ahn

Published Jan 1, 2017• 3 citations
Publisher

Abstract

N = 19 rubidium atoms are loaded with holographic optical tweezers in a zig-zag chain and entangled through collective Rabi oscillation to Rydberg state. Resulting coherent dynamics manifests quantum simulation of 1D quantum-Ising model with controlled frustrations.
DOI
10.1364/cleo_at.2017.jth5c.1

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•Dec 5, 2022•0 citations
Experimentally observed quantum few-body dynamics of neutral atoms excited to a Rydberg state are numerically analyzed. For this, up to five rubidium atoms are trapped with optical tweezers, arranged in various two-dimensional configurations, and excited to the Rydberg 67S67S67S state in the nearest-neighbor blockade regime. Their coherent evolutions are measured with time-varying ground-state projections and the experimental results are analyzed with a model Lindblad equation with the homogeneous and inhomogeneous dampings determined by systematic and statistical error analysis. The coherent and dissipative dynamics of these entangled systems are successfully reproduced using the given model and external parameters optimally calibrated with the experimental results.
Individually trapped neutral atoms are a promising candidate for use in quantum computing and simulation applications. They are highly scalable, have long coherence times and can be entangled via strong dipole-dipole interactions by driving to highly excited Rydberg states. However, the fidelity of single atom operations as well as two-atom entangling operations is limited by intrinsic sources of decoherence such as atomic motion, as well as technical sources of noise such as laser intensity fluctuations and phase/frequency fluctuations. We study the effect of these factors on single atom Rabi oscillations and two-atom Rydberg blockaded Rabi oscillations, using perturbation theory and numerical simulation. We develop a window function approach which helps us qualitatively understand the significance of the different spectral components of the noise as well as quantitatively understand the dependence of the Rabi oscillation fidelity on Rabi frequency. This allows us to predict the maximum experimentally achievable fidelities using independent measurements of experimental parameters such as noise spectra and atomic temperature. Turning to the question of near-term scalability of the experimental system, we prototype and test a method of generating a ’ladder’ configuration of optical tweezers utilizing two independent lasers. Our setup allows us to fully tune the geometry of the ladder, namely the separation between the two rows, the angle between them, and their relative position along the axis of the ladder. This pseudo-2D configuration enables us to reach larger system sizes in the near future and allows us to access beyond 1D physics.
Quantum simulation offers the possibility to study quantum mechanical problems which are untraceable on classical computers. This thesis introduces a novel platform for quantum simulation and presents the first experimental realisation of single potassium atoms trapped in optical tweezers. Interactions between individual atoms are induced by strong energy shifts of atoms excited to states with large principal quantum number, so-called Rydberg states. Either direct excitation to Rydberg states or off-resonant dressing can be used to induce these interactions. We argue that potassium is well-suited for the implementation of Rydberg dressing, enabling simultaneous dressing of both ground states to engineer complex interactions. Using techniques to cool and trap cold atoms, single potassium atoms are prepared in arrays of optical tweezers. Raman sideband cooling reduces vibrational excitations and prepares the atoms close to the motional ground state. This cooling technique mitigates severe limitations for Rydberg dressing, arising from thermal broadening and inhomogeneous light shifts in the array of atoms. To directly excite atoms to Rydberg states, a high power laser setup with two cavity-enhanced frequency doubling stages is constructed, generating up to one Watt of ulta-violet light at 286 nm. By exciting atoms to Rydberg states we observe Rabi oscillations with Rabi frequencies of up to 1 MHz, demonstrating coherent control of Rydberg atoms. Finally, we combine these techniques to observe interactions in two ways: First, we create a so-called superatom of up to four individual atoms using direct excitation and Rydberg-blockade and observe coherent oscillations to this collective state. We measure the expected square root scaling of the effective Rabi frequency with the number of individual atoms, confirming the creation of a many-body entangled state. Secondly, we off-resonantly dress the atoms prepared in a one-dimensional chain and measure correlated interaction shifts over multiple sites. In summary, we have developed a platform for quantum simulation with single atoms in optical tweezers. The presented results show coherent control of single atoms and interactions induced by Rydberg states. We have thus demonstrated that the system is well-suited for quantum simulation of many-body systems.
Neutral Rydberg atoms trapped in optical tweezer arrays provide a platform for quantum simulation and computation. In this work, we investigate the Lamb-Dicke dynamics of coupled Rydberg atoms for different trapping frequencies. We model the atomic motion by both internal and motional degrees of freedom, in which the motional states arise due to the oscillation of each atom in optical tweezer traps due to the light-atom interaction. In this setup, the internal states are coupled to a laser light with a Rabi frequency, while each internal state of each atom is also harmonically trapped with a trap frequency that depends on the internal state. The impact of the coherent motion of the optical tweezers on the collective dynamics of the many-body Rydberg atoms is explored for varying Lamb-Dicke parameters and with different trap frequencies. We see the occurrence of dynamical phases e.g., Rabi oscillations in the decoupled limit, the limit torus phase for magic trapping, and the limit cycle phase as the trap frequency is further increased.
We demonstrate three-dimensional trapping of individual Rydberg atoms in holographic optical bottle beam traps. Starting with cold, ground-state ^{87}Rb atoms held in standard optical tweezers, we excite them to nS_{1/2}, nP_{1/2}, or nD_{3/2} Rydberg states and transfer them to a hollow trap at 850 nm. For principal quantum numbers 60≤n≤90, the measured trapping time coincides with the Rydberg state lifetime in a 300 K environment. We show that these traps are compatible with quantum information and simulation tasks by performing single qubit microwave Rabi flopping, as well as by measuring the interaction-induced, coherent spin-exchange dynamics between two trapped Rydberg atoms separated by 40 μm. These results will find applications in the realization of high-fidelity quantum simulations and quantum logic operations with Rydberg atoms.
Quantum simulation offers interesting perspectives for the understanding of complex systems that are out of reach for numerical approaches. In this line, a new quantum simulation platform has recently been proposed. A spin-1/2 XXZ hamiltonian is thus realized in which the parameters can be controlled over a large range. The spin states are encoded by circular Rydberg states coupled through dipole-dipole interaction. These states benefit from longer lifetimes compared to the low angular momentum states used for current quantum simulations. In addition, they can be laser-trapped through the ponderomotive effect, and their lifetime can be further enhanced by spontaneous emission inhibition. We present in this thesis the first step towards the implementation of the proposed quantum simulator. We first prepare an array of rubidium 87 atoms trapped individually in optical tweezers. These atoms are subsequently excited to the circular Rydberg state n = 52 and transferred to hollow bottle-beam traps. We thus demonstrate the ponderomotive trapping of these states over durations of several milliseconds. We take advantage of the optical detection of the states thus prepared with various experiments. We characterize the trapping potential by measuring its transverse frequency. We finally conclude with the coherent manipulation of these trapped circular states through Rabi oscillations and Ramsey interferometry to determine their coherence.