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arXiv:2004.11412 · Physical Review A

Simulation of the complex dynamics of mean-field p -spin models using measurement-based quantum feedback control

Manuel H. Muñoz-Arias, Ivan Deutsch, Poul Jessen, Pablo M. Poggi

Published Aug 10, 2020• 23 citations
arXivHTMLPDF

Abstract

We study the application of a new method for simulating nonlinear dynamics of many-body spin systems using quantum measurement and feedback [Mu\~noz-Arias et al., Phys. Rev. Lett. 124, 110503 (2020)] to a broad class of many-body models known as $p$-spin Hamiltonians, which describe Ising-like models on a completely connected graph with $p$-body interactions. The method simulates the desired mean-field dynamics in the thermodynamic limit by combining nonprojective measurements of a component of the collective spin with a global rotation conditioned on the measurement outcome. We apply this protocol to simulate the dynamics of the $p$-spin Hamiltonians and demonstrate how different aspects of criticality in the mean-field regime are readily accessible with our protocol. We study applications including properties of dynamical phase transitions and the emergence of spontaneous symmetry breaking in the adiabatic dynamics of the collective spin for different values of the parameter $p$. We also demonstrate how this method can be employed to study the quantum-to-classical transition in the dynamics continuously as a function of system size.

DOI
10.1103/physreva.102.022610

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We study the application of a new method for simulating nonlinear dynamics of many-body spin systems using quantum measurement and feedback [Mu~noz-Arias et al., Phys. Rev. Lett. 124, 110503 (2020)] to a broad class of many-body models known as ppp-spin Hamiltonians, which describe Ising-like models on a completely connected graph with ppp-body interactions. The method simulates the desired mean-field dynamics in the thermodynamic limit by combining nonprojective measurements of a component of the collective spin with a global rotation conditioned on the measurement outcome. We apply this protocol to simulate the dynamics of the ppp-spin Hamiltonians and demonstrate how different aspects of criticality in the mean-field regime are readily accessible with our protocol. We study applications including properties of dynamical phase transitions and the emergence of spontaneous symmetry breaking in the adiabatic dynamics of the collective spin for different values of the parameter ppp. We also demonstrate how this method can be employed to study the quantum-to-classical transition in the dynamics continuously as a function of system size.
We study a method to simulate quantum many-body dynamics of spin ensembles using measurement-based feedback. By performing a weak collective measurement on a large ensemble of two-level quantum systems and applying global rotations conditioned on the measurement outcome, one can simulate the dynamics of a mean-field quantum kicked top, a standard paradigm of quantum chaos. We analytically show that there exists a regime in which individual quantum trajectories adequately recover the classical limit, and show the transition between noisy quantum dynamics to full deterministic chaos described by classical Lyapunov exponents. We also analyze the effects of decoherence, and show that the proposed scheme represents a robust method to explore the emergence of chaos from complex quantum dynamics in a realistic experimental platform based on an atom-light interface.
Abstract Non-equilibrium phase transitions are a vibrant frontier in physics, driving breakthroughs across diverse disciplines in recent years. Thermal spin ensembles, a captivating many-body quantum system, have harnessed their collective strengths to set remarkable measurement benchmarks in equilibrium. However, their non-equilibrium dynamics remain unexplored, with nonlinear interactions among constituents offering a rich playground for phase transition studies. Here, we employ nonlinear magnetic feedback to achieve real-time observation and control of phase transitions in a driven-dissipative spin ensemble, unveiling dynamic shifts between limit cycles, subharmonics, and chaos. This work not only deepens our grasp of critical phenomena in non-equilibrium systems but also paves the way for chaos-based sensing and information processing technologies, bridging fundamental physics with transformative applications.
A stochastic dynamical system is a system composed of many interacting components which includes stochastic behavior. Feedback control theory is designed to use information from the current state of the system in order to temper the final state toward the desired outcome. In this dissertation, I perform studies on two choices of classic and quantum dynamical systems to cover vast variety of statistical tools and methods. For classical model, I perform a study on finite-size effects at the phase transition in the Nagel-Schreckenberg traffic model as an example of non-equilibrium many body stochastic dynamical system. For quantum mechanical model, I introduce an optimal measurement-based feedback control protocol for cooling a single qubit as an example of complex system with one cell and many degrees of freedom. I examine the Nagel-Schreckenberg traffic model for a variety of maximum speeds. I show that the low density limit can be described as a dilute gas of vehicles with a repulsive core. At the transition to jamming, I observe finite-size effects in a variety of quantities describing the flow and the density correlations, but only if the maximum speed Vmax is larger than a certain value. A finite-size scaling analysis of several order parameters shows universal behavior, with scaling exponents that depend on Vmax The jamming transition at large Vmax can be viewed as the nucleation of jams in a background of freely flowing vehicles. Feedback control of quantum systems via continuous measurements involves complex nonlinear dynamics. As a result, even for a single qubit the optimal measurement for feedback control is known only in very special cases. I show here that for a broad class of noise processes, a series of compelling arguments can be applied to greatly simplify the problem of steady-state preparation of the ground-state, while loosing little in the way of optimality. Using numerical optimization to solve this simplified control problem, I obtain for the first time a non-trivial feedback protocol valid for all feedback strengths in the regime of good control. The protocol can be described relatively simply, and contains a discontinuity as a function of feedback strength.
Certain classes of quantum many-body systems, including those supporting phenomena like high-TcT_cTc​ superconductivity and spin liquids, are believed to be fundamentally intractable to classical modeling. Quantum simulations, in which synthetic materials are engineered by inducing well-controlled quantum systems like ultracold atoms to obey many-body Hamiltonians of interest, are a promising new approach to study this type of physics. In this work, I present several advances toward this ultimate goal of large-scale, highly controllable quantum simulations of many-body spin physics. We simulate long-range Ising and XY spin models in the presence of transverse and longitudinal magnetic fields using chains of up to 18 ultracold 171^{171}171Yb+^++ ions held in a linear Paul trap, where two hyperfine levels in each ion encode spin-1/2 states. The tunable spin-spin interactions and effective magnetic fields are engineered using laser fields, and the individual spin states are directly imaged with state-dependent fluorescence. The results in this thesis address several of the ongoing challenges in the development of synthetic quantum matter platforms. One such challenge is establishing more flexible capabilities in the sorts of Hamiltonians we can model. By observing suppression of the ground state spin ordering, we have demonstrated our ability to continuously tune the interaction range in a power-law interaction pattern, and hence the amount of frustration present in the spin system. We have additionally begun developing tools to study particles of higher spin, which could eventually be used to create and study topological phases of matter. Another challenge is the necessity of identifying problems that the next generation of experiments, with flexible (but not arbitrary) controls and classically intractable (but not infinitely large) system sizes, can feasibly shed new light on. We have made measurements of how the range of interaction affects dynamics of spin correlations propagating through the chain, and the excellent agreement between our observations and numerical simulations indicate that at larger sizes, our experiment can meaningfully contribute to the open question of the fundamental speed limit on the transfer of information through such a spin chain. Finally, for classically intractable system sizes, it will be crucial to have multiple techniques at our disposal for validating our understanding of the exact microscopic model being implemented. We have developed and demonstrated an MRI-like spectroscopic technique for probing the energies of the many-body Hamiltonian, which serves as a new method for validating quantum simulations of the transverse Ising model. Our experiments can potentially be scaled up in the near future to study fully connected lattice spin models with several tens of spins, where classical computation begins to fail, and the results described in this thesis contribute to the effort to build experiments that can break new ground in the study of quantum many-body physics.
We shift the paradigm of feedback control from the control of quantum states to the control of phase transitions in quantum systems. We show that feedback allows tuning the universality class of phase transitions via modifying its critical exponent. We expand our previous treatment [Ivanov et al., Phys. Rev. Lett. 124, 010603 (2020)] of the Dicke model and go beyond the approximation of the adiabatically eliminated light field. Both linearized and nonlinear models of spin ensembles are considered. The tunability of quantum fluctuations near the critical point by the feedbacks of nontrivial shapes is explained by considering the fluctuation spectra and the system behavior at single quantum trajectories.
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