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arXiv:1507.02553 · Mathematics for industry

Quantum Simulation of Spin Chains Coupled to Bosonic Modes with Superconducting Circuits

U. Las Heras, Laura García-Álvarez, Antonio Mezzacapo, E. Solano, Lucas Lamata

Published Sep 18, 2015• 1 citation
arXivHTMLPDF
DOI
10.1007/978-4-431-55342-7_8

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We consider superconducting circuits for the purpose of simulating the spin-boson model. The spin-boson model consists of a single two-level system coupled to bosonic modes. In most cases, the model is considered in a limit where the bosonic modes are sufficiently dense to form a continuous spectral bath. A very well known case is the Ohmic bath, where the density of states grows linearly with the frequency. In the limit of weak coupling or large temperature, this problem can be solved numerically. If the coupling is strong, the bosonic modes can become sufficiently excited to make a classical simulation impossible. Here we discuss how a quantum simulation of this problem can be performed by coupling a superconducting qubit to a set of microwave resonators. We demonstrate a possible implementation of a continuous spectral bath with individual bath resonators coupling strongly to the qubit. Applying a microwave drive scheme potentially allows us to access the strong-coupling regime of the spin-boson model. We discuss how the resulting spin relaxation dynamics with different initialization conditions can be probed by standard qubit-readout techniques from circuit quantum electrodynamics.
The ground state of a pair of ultrastrongly coupled bosonic modes is predicted to be a two-mode squeezed vacuum. However, the corresponding quantum correlations are currently unobservable in condensed matter where such a coupling can be reached, since it cannot be extracted from these systems. Here, we show that superconducting circuits can be used to perform an analog simulation of a system of two bosonic modes in regimes ranging from strong to ultrastrong coupling. More importantly, our quantum simulation setup enables us to detect output excitations that are related to the ground-state properties of the bosonic modes. We compute the emission spectra of this physical system and show that the produced state presents single- and two-mode squeezing simultaneously.
We propose a digital-analog quantum simulation of generalized Dicke models with superconducting circuits, including Fermi- Bose condensates, biased and pulsed Dicke models, for all regimes of light-matter coupling. We encode these classes of problems in a set of superconducting qubits coupled with a bosonic mode implemented by a transmission line resonator. Via digital-analog techniques, an efficient quantum simulation can be performed in state-of-the-art circuit quantum electrodynamics platforms, by suitable decomposition into analog qubit-bosonic blocks and collective single-qubit pulses through digital steps. Moreover, just a single global analog block would be needed during the whole protocol in most of the cases, superimposed with fast periodic pulses to rotate and detune the qubits. Therefore, a large number of digital steps may be attained with this approach, providing a reduced digital error. Additionally, the number of gates per digital step does not grow with the number of qubits, rendering the simulation efficient. This strategy paves the way for the scalable digital-analog quantum simulation of many-body dynamics involving bosonic modes and spin degrees of freedom with superconducting circuits.