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arXiv:1711.07392

Exploring adiabatic quantum dynamics of the Dicke model in a trapped ion quantum simulator

Arghavan Safavi-Naini, Robert J. Lewis-Swan, Justin Bohnet, Martin Gärttner, Kevin Gilmore, Jordan, E., Jeffrey Cohn, James K. Freericks, A. M. Rey, J. J. Bollinger

Published Nov 20, 2017• 9 citations
arXivHTMLPDF

Abstract

We use a self-assembled two-dimensional Coulomb crystal of $\sim 70$ ions in the presence of an external transverse field to engineer a quantum simulator of the Dicke Hamiltonian. This Hamiltonian has spin and bosonic degrees of freedom which are encoded by two hyperfine states in each ion and the center of mass motional mode of the crystal, respectively. The Dicke model features a quantum critical point separating two distinct phases: the superradiant (ferromagnetic) and normal (paramagnetic) phases. We experimentally explore protocols that aim to adiabatically prepare the superradiant ground state, a spin-boson cat state with macroscopic phonon occupation, which is well-suited for enhanced metrology and quantum information processing. We start in the normal phase, with all spins aligned along a large transverse field and ramp down the field across the critical point following various protocols. We measure the spin observables, both experimentally and in our simulations to characterize the state of the system at the end of the ramp. We find that under current operating conditions an optimally designed ramp is not sufficient to achieve significant fidelity with the superradiant ground state. However, our theoretical investigation shows that slight modifications of experimental parameters, together with modest reductions in decoherence rates and thermal noise can increase the cat-state fidelity to $\sim 75\%$ for $N \sim 20$ spins. Our results open a path for the use of large ensembles of trapped ions as powerful quantum sensors and quantum computers.

DOI
10.48550/arxiv.1711.07392

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•Jan 1, 2016•1 citation
We use a self-assembled two-dimensional Coulomb crystal of ∼70\sim 70∼70 ions in the presence of an external transverse field to engineer a quantum simulator of the Dicke Hamiltonian. This Hamiltonian has spin and bosonic degrees of freedom which are encoded by two hyperfine states in each ion and the center of mass motional mode of the crystal, respectively. The Dicke model features a quantum critical point separating two distinct phases: the superradiant (ferromagnetic) and normal (paramagnetic) phases. We experimentally explore protocols that aim to adiabatically prepare the superradiant ground state, a spin-boson cat state with macroscopic phonon occupation, which is well-suited for enhanced metrology and quantum information processing. We start in the normal phase, with all spins aligned along a large transverse field and ramp down the field across the critical point following various protocols. We measure the spin observables, both experimentally and in our simulations to characterize the state of the system at the end of the ramp. We find that under current operating conditions an optimally designed ramp is not sufficient to achieve significant fidelity with the superradiant ground state. However, our theoretical investigation shows that slight modifications of experimental parameters, together with modest reductions in decoherence rates and thermal noise can increase the cat-state fidelity to ∼75%\sim 75\%∼75% for N∼20N \sim 20N∼20 spins. Our results open a path for the use of large ensembles of trapped ions as powerful quantum sensors and quantum computers.
We use a self-assembled two-dimensional Coulomb crystal of ∼70 ions in the presence of an external transverse field to engineer a simulator of the Dicke Hamiltonian, an iconic model in quantum optics which features a quantum phase transition between a superradiant (ferromagnetic) and a normal (paramagnetic) phase. We experimentally implement slow quenches across the quantum critical point and benchmark the dynamics and the performance of the simulator through extensive theory-experiment comparisons which show excellent agreement. The implementation of the Dicke model in fully controllable trapped ion arrays can open a path for the generation of highly entangled states useful for enhanced metrology and the observation of scrambling and quantum chaos in a many-body system.
Quantum many-body systems driven far from equilibrium can exhibit phase transitions, chaos and entanglement, but probing these phenomena in large, nearly closed systems remains challenging. The Dicke model, which couples an ensemble of two-level systems collectively to a single bosonic mode, provides a fundamental framework for exploring these phenomena in light-matter interactions. Here we show that a two-dimensional crystal of approximately 100 trapped ions realizes this model and accesses integrable dynamical phase transitions, signatures of chaotic dynamics and fluctuation-driven spin-phonon excitation growth. Adiabatic elimination of the vibrational mode reveals ferromagnetic and paramagnetic dynamical spin phases, whereas strong spin-phonon coupling produces irregular trajectories and local relaxation consistent with quantum thermalization. Following a quench from an unstable fixed point, correlated excitation growth precedes generalized vacuum Rabi collapses and revivals; calibrated calculations identify two-mode squeezing 2.6 dB below the standard quantum limit, supported by reconstruction from spin measurements. By connecting collective dynamical instabilities to experimentally accessible signatures of quantum correlations, these results establish large ion crystals as a scalable platform for investigating non-equilibrium light-matter dynamics and generating resources for quantum-enhanced sensing.
Temporal non-analyticities in the rate function of the Loschmidt echo manifests a class of dynamical quantum phase transitions (DQPTs) that has emerged as a powerful framework for understanding far-from-equilibrium many-body dynamics. While such DQPT has been extensively studied theoretically in spin-boson systems such as the Dicke model, their experimental observation remains elusive. In particular, the dynamics of DQPT in asymmetric spin subspaces and under the influence of spin dissipation are largely unexplored. Here, we report an experimental study of temporal DQPT in a generalized Dicke model using a trapped-ion quantum simulator. By coupling a linear chain of 40Ca+\rm{^{40}Ca^{+}}40Ca+ ions to a collective center-of-mass motional mode, we probe the quench dynamics starting from both symmetric and asymmetric initial states. We extract the rate function and identify temporal turn-around points that are in quantitative agreement with theoretical predictions. Additionally, we investigate the impact of spin dissipation on these dynamics. Our results establish an experimental platform for probing complex many-body out-of-equilibrium phenomena and advance the development of hybrid oscillator-spin quantum simulators.
In a proof-of-principle experiment, we simulate the dynamics of a quantum spin system in an ion trap. Following a theoretical proposal by D. Porras and I. Cirac, we use a system of ground state cooled trapped ions to simulate and study the dynamics of a quantum-mechanical system, or more precisely, the dynamics of a quantum spin Hamiltonian. We implement the smallest non-trivial quantum spin Hamiltonian, the quantum Ising model for two spins. Each spin is represented by two hyperfine ground levels of trapped 25Mg+ ions. The interaction with an external magnetic field is simulated by coherently coupling these hyperfine levels via laser and radiofrequency radiation. The spin-spin interaction is simulated via optical dipole forces, where the effective interaction is mediated by the phonons of the linear ion chain. We demonstrate the adiabatic evolution from a paramagnetically ordered system to ferromagnetic order. The final state of this adiabatic transition is a superposition state of the two degenerate spin configurations of ferromagnetic order Psi_final = 1/sqrt(2) (|up up> + |down down>) with a quantum magnetisation of 98%. We also show the transition from paramagnetic to antiferromagnetic order with the final state Psi_final = 1/sqrt(2) (|up down> + |down up>). Moreover, we prove that this transition which is to become a quantum phase transition in the thermodynamic limit of infinitely many spins, is driven by quantum fluctuations which dominate the dynamics of such systems at the absolute zero-point of temperature rather than thermal fluctuations which are absent at 0 K. This is verified by the fact that the final state of our adiabatic evolution is entangled, close to a Bell state at a fidelity exceeding 88%. The set of tools presented in this thesis might serve as a basis for larger scale quantum simulations which might help in gaining insight into many-particle effects that are intractable on classical computers such as spin frustration in triangular lattices or high-Tc superconductivity.
We investigate a generalized Dicke model by introducing two interacting spin ensembles coupled with a single-mode bosonic field. Apart from the normal to superradiant phase transition induced by the strong spin-boson coupling, interactions between the two spin ensembles enrich the phase diagram by introducing ferromagnetic, antiferromagnetic and paramagnetic phases. The mean-field approach reveals a phase diagram comprising three phases: paramagnetic-normal phase, ferromagnetic-superradiant phase, and antiferromagnetic-normal phase. Ferromagnetic spin-spin interaction can significantly reduce the required spin-boson coupling strength to observe the superradiant phase, where the macroscopic excitation of the bosonic field occurs. Conversely, antiferromagnetic spin-spin interaction can strongly suppress the superradiant phase. To examine higher-order quantum effects beyond the mean-field contribution, we utilize the Holstein-Primakoff transformation, which converts the generalized Dicke model into three coupled harmonic oscillators in the thermodynamic limit. Near the critical point, we observe the close of the energy gap between the ground and the first excited states, the divergence of entanglement entropy and quantum fluctuation in certain quadrature. These observations further confirm the quantum phase transition and offer additional insights into critical behaviors.
While fault-tolerant quantum computation might still be years away, analog quantum simulators offer a way to leverage current quantum technologies to study classically intractable quantum systems. Cutting edge quantum simulators such as those utilizing ultracold atoms are beginning to study physics which surpass what is classically tractable. As the system sizes of these quantum simulators increase, there are also concurrent gains in the complexity and types of Hamiltonians which can be simulated. In this work, I describe advances toward the realization of an adaptable, tunable quantum simulator capable of surpassing classical computation. We simulate long-ranged Ising and XY spin models which can have global arbitrary transverse and longitudinal fields in addition to individual transverse fields using a linear chain of up to 24 Yb+ 171 ions confined in a linear rf Paul trap. Each qubit is encoded in the ground state hyperfine levels of an ion. Spin-spin interactions are engineered by the application of spin-dependent forces from laser fields, coupling spin to motion. Each spin can be read independently using state-dependent fluorescence. The results here add yet more tools to an ever growing quantum simulation toolbox. One of many challenges has been the coherent manipulation of individual qubits. By using a surprisingly large fourth-order Stark shifts in a clock-state qubit, we demonstrate an ability to individually manipulate spins and apply independent Hamiltonian terms, greatly increasing the range of quantum simulations which can be implemented. As quantum systems grow beyond the capability of classical numerics, a constant question is how to verify a quantum simulation. Here, I present measurements which may provide useful metrics for large system sizes and demonstrate them in a system of up to 24 ions during a classically intractable simulation. The observed values are consistent with extremely large entangled states, as much as ~95% of the system entangled. Finally, we use many of these techniques in order to generate a spin Hamiltonian which fails to thermalize during experimental time scales due to a meta-stable state which is often called prethermal. The observed prethermal state is a new form of prethermalization which arises due to long-range interactions and open boundary conditions, even in the thermodynamic limit. This prethermalization is observed in a system of up to 22 spins. We expect that system sizes can be extended up to 30 spins with only minor upgrades to the current apparatus. These results emphasize that as the technology improves, the techniques and tools developed here can potentially be used to perform simulations which will surpass the capability of even the most sophisticated classical techniques, enabling the study of a whole new regime of quantum many-body physics.