Criticality-based quantum metrology in the presence of decoherence

doi:10.1007/s11467-023-1278-2

Front. Phys.

2023, Vol. 18

Issue (3) : 31304 https://doi.org/10.1007/s11467-023-1278-2

RESEARCH ARTICLE

Criticality-based quantum metrology in the presence of decoherence

Wan-Ting He, Cong-Wei Lu, Yi-Xuan Yao, Hai-Yuan Zhu, Qing Ai(

)

Department of Physics, Applied Optics Beijing Area Major Laboratory, Beijing Normal University, Beijing 100875, China

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Abstract

Because quantum critical systems are very sensitive to the variation of parameters around the quantum phase transition (QPT), quantum criticality has been presented as an efficient resource for metrology. In this paper, we address the issue whether the divergent feature of the inverted variance is realizable in the presence of noise when approaching the QPT. Taking the quantum Rabi model (QRM) as an example, we obtain the analytical result for the inverted variance with single-photon relaxation. We show that the inverted variance may be convergent in time due to the noise. Since the precision of the metrology is very sensitive to the noise, as a remedy, we propose squeezing the initial state to improve the precision under decoherence. In addition, we also investigate the criticality-based metrology under the influence of the two-photon relaxation. Strikingly, although the maximum inverted variance still manifests a power-law dependence on the energy gap, the exponent is positive and depends on the dimensionless coupling strength. This observation implies that the criticality may not enhance but weaken the precision in the presence of two-photon relaxation, due to the non-linearity introduced by the two-photon relaxation.

Keywords criticality quantum metrology decoherence

Corresponding Author(s): Qing Ai

Issue Date: 07 April 2023

Cite this article:

Wan-Ting He,Cong-Wei Lu,Yi-Xuan Yao, et al. Criticality-based quantum metrology in the presence of decoherence[J]. Front. Phys. , 2023, 18(3): 31304.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-023-1278-2
https://academic.hep.com.cn/fop/EN/Y2023/V18/I3/31304

Fig.1 The effect of the noise strength

κ

on the precision of the criticality-enhanced metrology. (a) The inverted variance of the QRM in the vicinity of the critical point, e.g.,

g = 0.96

, when coupling with a thermal reservoir at zero temperature, for

100 κ / ω = 1, 2, 3, 4, 5

. They correspond to the blue solid, orange dashed, green dash-dotted, red dotted, purple solid line, respectively. (b) The maximum of the inverted variance as a function of the noise parameter

κ

. From the bottom to the top, the five curves correspond to

g = 0.94, 0.95, 0.96,

0.97, 0.98,

respectively. The dots are obtained from the master equation, while the curves are calculated by the numerical fitting.

Fig.2 The effect of the energy gap

Δ g

on the precision of the criticality-enhanced metrology. (a) The inverted variance

F g

of the QRM when approaching the critical point, e.g.

g = 0.94, 0.95, 0.96, 0.97, 0.98

, with the noise parameter

κ = 0.05 ω

. It is plotted against the rescaled time

Δ g ω t / (2 π)

to highlight the behavior that in the representation of the rescaled time

F g

’s oscillate with the same frequency for different

g

’s. (b) The maximum of

F g

vs.

Δ g

for

100 κ / ω = 1, 2, 3, 4, 5

, which correspond to the curves from the top to the bottom. The dots are obtained from the master equation, while the curves are calculated by the numerical fitting.

Fig.3 The effect of the temperature

T

on the precision of the criticality-enhanced metrology. (a) The inverted variance of the QRM close to the critical point, at

g = 0.96

, with

n ˉ = 1, 2, 3, 4, 5

and

κ / ω = 0.05

. (b) The maximum inverted variance vs. the temperature

T

. The balck dotted line is numerically fitted by

a (k B T / ω) b

with

a = 2648

and

b = ? 0.953

Fig.4 Improving the precision by performing a squeezing operation on the initial state. (a)

F g (t)

versus time

t

, with different squeezing parameter

ξ

, when

g = 0.96

and

κ / ω = 0.05

. (b) The maximum of

F g

at different

ξ

’s with

100 κ / ω =

1, 2, 3, 4, 5

Fig.5 The effects of the squeezing parameter

ξ

. (a) At zero temperature, the maxima of

F g

vs.

κ

when

g = 0.96

and

ξ = 0, 0.4, 0.8, 1.2, 1.6, 2

, which correspond to the curves from the bottom to the top. (b) The maximum of

F g

at different

ξ

's for

k B T / ω = 0, 1, 2, 3, 4, 5

, which correspond to the curves from the top to the bottom. The dots are obtained from the master equation, while the curves are calculated by the numerical fitting.

Fig.6 The effects of the two-photon relaxation. (a) The inverted variance

F g

of the QRM when approaching the critical point, e.g.,

g = 0.94, 0.95, 0.96, 0.97, 0.98

, with the noise parameter

κ = 0.05 ω

. It is plotted against the rescaled time

1 ? g 2 ω t / π

. (b) The maximum of

F g

at different

g

’s with

100 κ / ω =

1, 2, 3, 4, 5

. The dots are obtained from the master equation, while the curves are calculated by the numerical fitting.

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