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arXiv:1807.11285 · Physical Review A

Cooling of many-body systems via selective interactions

Roberto Grimaudo, Lucas Lamata, E. Solano, ANTONINO MESSINA

Published Oct 23, 2018• 20 citations
arXivHTMLPDF

Abstract

We propose a model describing $N$ spin-1/2 systems coupled through $N$-order homogeneous interaction terms, in the presence of local time-dependent magnetic fields. This model can be experimentally implemented with current technologies in trapped ions and superconducting circuits. By introducing a chain of unitary transformations, we succeed in exactly converting the quantum dynamics of this system into that of ${2}^{N\ensuremath{-}1}$ fictitious spin-1/2 dynamical problems. We bring to light the possibility of controlling the unitary evolution of the $N$ spins generating Greenberger-Horne-Zeilinger states under specific time-dependent scenarios. Moreover, we show that by appropriately engineering the time dependence of the coupling parameters, one may choose a specific subspace in which the $N$-spin system dynamics takes place. This dynamical feature, which we call time-dependent selective interaction, can generate a cooling effect of all spins in the system.

DOI
10.1103/physreva.98.042330

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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 propose a method to create selective interactions with Dicke-Stark model by means of a time-dependent perturbation theory. By choosing the proper rotating framework, we find that the time oscillating terms depend on the number of atomic excitations and the number of photonic excitations. Consequently, the Rabi oscillation between selective states can be realized by properly choosing the frequency of the two-level system. The second order selective interactions can also be studied with this method. Then various states, such as Dicke states, superposition of Dicke states and GHZ states, can be created by means of such selective interactions. The numerical results show that high fidelity Dicke states and Greenberger-Horne-Zeilinger states can be created by choosing the proper frequency of the two-level system and controlling the evolution time.
Abstract A protocol for generating Greenberger‐Horne‐Zeilinger states in a system of coupled qubits is proposed. The Hamiltonian model assumes ‐wise interactions between the qubits and the presence of a controllable time‐dependent field acting upon one spin only. The dynamical problem is exactly solved thanks to the symmetries of the Hamiltonian model. The possibility of generating GHZ states simulating our physical scenario under both adiabatic and non‐adiabatic conditions is within the reach of the experimentalists. This aspect is discussed in detail.
The physics of interacting integer-spin chains has been a topic of intense theoretical interest, particularly in the context of symmetry-protected topological phases.However, there has not been a controllable model system to study this physics experimentally.We demonstrate how spin-dependent forces on trapped ions can be used to engineer an effective system of interacting spin-1 particles.Our system evolves coherently under an applied spin-1 XY Hamiltonian with tunable, long-range couplings, and all three quantum levels at each site participate in the dynamics.We observe the time evolution of the system and verify its coherence by entangling a pair of effective three-level particles ("qutrits") with 86% fidelity.By adiabatically ramping a global field, we produce ground states of the XY model, and we demonstrate an instance where the ground state cannot be created without breaking the same symmetries that protect the topological Haldane phase.This experimental platform enables future studies of symmetry-protected order in spin-1 systems and their use in quantum applications.
The physics of interacting integer-spin chains has been a topic of intense theoretical interest, particularly in the context of symmetry-protected topological phases. However, there has not been a controllable model system to study this physics experimentally. We demonstrate how spin-dependent forces on trapped ions can be used to engineer an effective system of interacting spin-1 particles. Our system evolves coherently under an applied spin-1 XY Hamiltonian with tunable, long-range couplings, and all three quantum levels at each site participate in the dynamics. We observe the time evolution of the system and verify its coherence by entangling a pair of effective three-level particles (“qutrits”) with 86% fidelity. By adiabatically ramping a global field, we produce ground states of the XY model, and we demonstrate an instance where the ground state cannot be created without breaking the same symmetries that protect the topological Haldane phase. This experimental platform enables future studies of symmetry-protected order in spin-1 systems and their use in quantum applications.
By coupling pairs of superconducting qubits through a small Josephson junction with a time-dependent flux bias, we show that arbitrary interactions involving any combination of Pauli matrices can be generated with a small number of drive tones applied through the flux bias of the coupling junction. We then demonstrate that similar (though not fully universal) results can be achieved in capacitively coupled qubits by exploiting the higher energy states of the devices through multiphoton drive signals applied to the qubits' flux degrees of freedom. By using this mechanism to couple a qubit to a detuned resonator, the qubit's rotating-frame state can be nondestructively measured along any direction on the Bloch sphere. Finally, we describe how the frequency-converting nature of the couplings can be used to engineer a mechanism analogous to dynamic nuclear polarization in NMR systems, capable of cooling an array of qubits well below the ambient temperature, and outline how higher-order interactions, such as local three-body terms, can be engineered through the same couplings. Our results demonstrate that a programmable quantum simulator for large classes of interacting spin models could be engineered with the same physical hardware.