TY - JOUR
T1 - Long-Time Relaxation of a Finite Spin Bath Linearly Coupled to a Qubit
AU - Pekola, Jukka P.
AU - Karimi, Bayan
AU - Cattaneo, Marco
AU - Maniscalco, Sabrina
N1 - Publisher Copyright:
© 2023 World Scientific Publishing Company.
PY - 2023/6/1
Y1 - 2023/6/1
N2 - We discuss the long-time relaxation of a qubit linearly coupled to a finite bath of N spins (two-level systems, TLSs), with the interaction Hamiltonian in rotating wave approximation. We focus on the regime N≫1,
assuming that the qubit–bath coupling is weak, that the range of spin
frequencies is sufficiently broad, and that all the spins are
initialized in the ground state. Despite the model being perfectly
integrable, we make two interesting observations about the effective
system relaxation. First, as one would expect, the qubit relaxes
exponentially towards its zero-temperature state at a well characterized
rate. Second, the bath spins, even when mutually coupled, do not relax
towards a thermal distribution, but rather form a Lorentzian
distribution peaked at the frequency of the initially excited qubit.
This behaviour is captured by an analytical approximation that makes use
of the property N≫1 to treat the TLS frequencies as a continuum and is confirmed by our numerical simulations.
AB - We discuss the long-time relaxation of a qubit linearly coupled to a finite bath of N spins (two-level systems, TLSs), with the interaction Hamiltonian in rotating wave approximation. We focus on the regime N≫1,
assuming that the qubit–bath coupling is weak, that the range of spin
frequencies is sufficiently broad, and that all the spins are
initialized in the ground state. Despite the model being perfectly
integrable, we make two interesting observations about the effective
system relaxation. First, as one would expect, the qubit relaxes
exponentially towards its zero-temperature state at a well characterized
rate. Second, the bath spins, even when mutually coupled, do not relax
towards a thermal distribution, but rather form a Lorentzian
distribution peaked at the frequency of the initially excited qubit.
This behaviour is captured by an analytical approximation that makes use
of the property N≫1 to treat the TLS frequencies as a continuum and is confirmed by our numerical simulations.
KW - finite baths
KW - Quantum thermalization
KW - spin baths
KW - superconducting qubit decay
UR - http://www.scopus.com/inward/record.url?scp=85166072510&partnerID=8YFLogxK
U2 - 10.1142/S1230161223500099
DO - 10.1142/S1230161223500099
M3 - Article
AN - SCOPUS:85166072510
SN - 1230-1612
VL - 30
JO - Open Systems and Information Dynamics
JF - Open Systems and Information Dynamics
IS - 2
M1 - 2350009
ER -