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Digital quantum Rabi and Dicke models in superconducting circuits.

Mezzacapo A, Las Heras U, Pedernales JS, DiCarlo L, Solano E, Lamata L - Sci Rep (2014)

Bottom Line: We find that all physical regimes, in particular those which are impossible to realize in typical cavity QED setups, can be simulated via unitary decomposition into digital steps.Furthermore, we show the emergence of the Dirac equation dynamics from the quantum Rabi model when the mode frequency vanishes.Finally, we analyze the feasibility of this proposal under realistic superconducting circuit scenarios.

View Article: PubMed Central - PubMed

Affiliation: Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, E-48080 Bilbao, Spain.

ABSTRACT
We propose the analog-digital quantum simulation of the quantum Rabi and Dicke models using circuit quantum electrodynamics (QED). We find that all physical regimes, in particular those which are impossible to realize in typical cavity QED setups, can be simulated via unitary decomposition into digital steps. Furthermore, we show the emergence of the Dirac equation dynamics from the quantum Rabi model when the mode frequency vanishes. Finally, we analyze the feasibility of this proposal under realistic superconducting circuit scenarios.

No MeSH data available.


Frequency scheme of the stepwise implementation for the quantum Rabi Hamiltonian.A transmon qubit of frequency ωq is interacting with a microwave resonator, whose transition frequency is ωr. The interactions H1,2 in Eq. (3) are simulated respectively with a Jaynes-Cummings interaction (step 1), and another one with different detuning, anticipated and followed by π pulses (step 2).
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f1: Frequency scheme of the stepwise implementation for the quantum Rabi Hamiltonian.A transmon qubit of frequency ωq is interacting with a microwave resonator, whose transition frequency is ωr. The interactions H1,2 in Eq. (3) are simulated respectively with a Jaynes-Cummings interaction (step 1), and another one with different detuning, anticipated and followed by π pulses (step 2).

Mentions: The quantum Rabi Hamiltonian in Eq. (2) can be decomposed into two parts, HR = H1 + H2, where and we have defined the qubit transition frequency in the two steps such that . These two interactions can be simulated in a typical circuit QED device with fast control of the qubit transition frequency. Starting from the qubit-resonator Hamiltonian in Eq. (1), one can define a frame rotating at frequency , in which the effective interaction Hamiltonian becomes with and . Therefore, Eq. (4) is equivalent to H1, following a proper redefinition of the coefficients. The counter-rotating term H2 can be simulated by applying a local qubit rotation to and a different detuning for the qubit transition frequency, By choosing different qubit-resonator detuning for the two steps, for the first one and for the rotated step, one is able to simulate the quantum Rabi Hamiltonian, Eq. (2), via digital decomposition21, by interleaving the simulated interactions. The frequency scheme of the protocol is shown in Fig. 1. Standard resonant Jaynes-Cummings interaction parts with different qubit transition frequencies are interrupted by microwave pulses, in order to perform customary qubit flips29. This sequence can be repeated according to the digital simulation scheme to obtain a better approximation of the quantum Rabi dynamics.


Digital quantum Rabi and Dicke models in superconducting circuits.

Mezzacapo A, Las Heras U, Pedernales JS, DiCarlo L, Solano E, Lamata L - Sci Rep (2014)

Frequency scheme of the stepwise implementation for the quantum Rabi Hamiltonian.A transmon qubit of frequency ωq is interacting with a microwave resonator, whose transition frequency is ωr. The interactions H1,2 in Eq. (3) are simulated respectively with a Jaynes-Cummings interaction (step 1), and another one with different detuning, anticipated and followed by π pulses (step 2).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4265784&req=5

f1: Frequency scheme of the stepwise implementation for the quantum Rabi Hamiltonian.A transmon qubit of frequency ωq is interacting with a microwave resonator, whose transition frequency is ωr. The interactions H1,2 in Eq. (3) are simulated respectively with a Jaynes-Cummings interaction (step 1), and another one with different detuning, anticipated and followed by π pulses (step 2).
Mentions: The quantum Rabi Hamiltonian in Eq. (2) can be decomposed into two parts, HR = H1 + H2, where and we have defined the qubit transition frequency in the two steps such that . These two interactions can be simulated in a typical circuit QED device with fast control of the qubit transition frequency. Starting from the qubit-resonator Hamiltonian in Eq. (1), one can define a frame rotating at frequency , in which the effective interaction Hamiltonian becomes with and . Therefore, Eq. (4) is equivalent to H1, following a proper redefinition of the coefficients. The counter-rotating term H2 can be simulated by applying a local qubit rotation to and a different detuning for the qubit transition frequency, By choosing different qubit-resonator detuning for the two steps, for the first one and for the rotated step, one is able to simulate the quantum Rabi Hamiltonian, Eq. (2), via digital decomposition21, by interleaving the simulated interactions. The frequency scheme of the protocol is shown in Fig. 1. Standard resonant Jaynes-Cummings interaction parts with different qubit transition frequencies are interrupted by microwave pulses, in order to perform customary qubit flips29. This sequence can be repeated according to the digital simulation scheme to obtain a better approximation of the quantum Rabi dynamics.

Bottom Line: We find that all physical regimes, in particular those which are impossible to realize in typical cavity QED setups, can be simulated via unitary decomposition into digital steps.Furthermore, we show the emergence of the Dirac equation dynamics from the quantum Rabi model when the mode frequency vanishes.Finally, we analyze the feasibility of this proposal under realistic superconducting circuit scenarios.

View Article: PubMed Central - PubMed

Affiliation: Department of Physical Chemistry, University of the Basque Country UPV/EHU, Apartado 644, E-48080 Bilbao, Spain.

ABSTRACT
We propose the analog-digital quantum simulation of the quantum Rabi and Dicke models using circuit quantum electrodynamics (QED). We find that all physical regimes, in particular those which are impossible to realize in typical cavity QED setups, can be simulated via unitary decomposition into digital steps. Furthermore, we show the emergence of the Dirac equation dynamics from the quantum Rabi model when the mode frequency vanishes. Finally, we analyze the feasibility of this proposal under realistic superconducting circuit scenarios.

No MeSH data available.