Vibrational resonance via a single-ion phonon laser

doi:10.15302/frontphys.2025.012203

Front. Phys.

2025, Vol. 20

Issue (1) : 12203 https://doi.org/10.15302/frontphys.2025.012203

Vibrational resonance via a single-ion phonon laser

Quan Yuan^1,², Shuang-Qing Dai^1,², Tai-Hao Cui^1,², Pei-Dong Li^1,², Yuan-Zhang Dong^1,², Ji Li^1,^2,³, Fei Zhou^1,³, Jian-Qi Zhang¹(

), Liang Chen^1,³(

), Mang Feng^1,^3,⁴(

)

¹. State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan 430071, China
². University of Chinese Academy of Sciences, Beijing 100049, China
³. Research Center for Quantum Precision Measurement, Guangzhou Institute of Industry Co., Ltd., Guangzhou 511458, China
⁴. Department of Physics, Zhejiang Normal University, Jinhua 321004, China

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Abstract

Vibrational resonances are ubiquitous in various nonlinear systems and play crucial roles in detecting weak low-frequency signals and developing highly sensitive sensors. Here we demonstrate vibrational resonance, for the first time, utilizing a single-ion phonon laser system exhibiting Van der Pol-type nonlinearity. To enhance the response of the phonon laser system to weak signals, we experimentally realize continuously tunable symmetry of the bistability in the phonon laser system via optical modulation, and achieve the maximum vibrational resonance amplification of 23 dB. In particular, our single-ion phonon laser system relaxes the frequency separation condition and exhibits the potential of multi-frequency signal amplification using the vibrational resonance. Our study employs the phonon laser to study and optimize the vibrational resonance with simple and well-controllable optical technology, which holds potential applications in developing precision metrology and single-ion sensors with on-chip ion traps.

Keywords single-ion phonon laser vibrational resonance nonlinear system

Corresponding Author(s): Jian-Qi Zhang,Liang Chen,Mang Feng

Just Accepted Date: 14 September 2024 Issue Date: 14 October 2024

Cite this article:

Quan Yuan,Shuang-Qing Dai,Tai-Hao Cui, et al. Vibrational resonance via a single-ion phonon laser[J]. Front. Phys. , 2025, 20(1): 12203.

URL:

https://academic.hep.com.cn/fop/EN/10.15302/frontphys.2025.012203
https://academic.hep.com.cn/fop/EN/Y2025/V20/I1/12203

Fig.1 Experimental setup and principle of tunable bistability. (a) Sketch of SET and single-ion phonon laser. (b) Schematic of experimental setup and the corresponding energy level scheme. After frequency and power adjustment by the AOMs, the three laser beams are then combined and introduced into the SET, where the solid arrows represent the laser beams and the corresponding transitions they couple (blue, red, and grey denote blue-tuned 397-nm laser, red-tuned 397-nm laser and 866-nm laser, respectively), the yellow wavy arrow represents the spontaneous emission. The amplitudes of the signals are transformed to frequency unit, with respect to the modulation depth of 3.6 MHz/Vpp. (c) The amplitude of the single ion’s oscillation versus the detuning

Δ

between the 397-nm laser and energy gap (for two energy-levels

42 S 1 / 2

and

42 P 1 / 2

) in a sweep-up (red solid line) and sweep-down (blue dashed line) experiment. The ion exhibits thermal motion

| t ?

and coherent motion

| c ?

corresponding to the lower and upper branches of the bistability, respectively. The yellow (blue) area represents the thermal (coherent) oscillation regime. (d) Distribution of photon counts of the ion collected by the PMT and relevant to the two stable states, which correspond to

Δ a

, with a driving set with frequency

Ω d / (2 π)

= 1 Hz and amplitude

ω d / (2 π)

= 2.16 MHz. With

Δ a / (2 π)

detuned to −0.75, 0, and 0.75 MHz, the ratios of frequency counts of the ion regarding the two states are 561:369, 468:462, 346:589, respectively.

Fig.2 VR in a Van der Pol oscillator. The response of the phonon laser with respect to the strength of the HF driving modulation, where the weak signal with the strength

ω s i g / (2 π) =

0.72 MHz is of the frequency

Ω s i g / (2 π) =

1 Hz and the HF modulation frequency is

Ω H F / (2 π) =

100 Hz. (a) The time trace of the photon counts acquired by the PMT and the corresponding FFT spectrum under the condition of a symmetric bistable system with

Δ a =

0, where the panels from top to bottom correspond to the HF driving strength of

ω H F / (2 π) =

0.72 MHz, 2.16 MHz, 2.88 MHz, 5.76 MHz, and 14.40 MHz. The blue (yellow) semitransparent area in the left panel represents the mean photon counts of the system in the phonon-laser (thermal) motion. The vertical dashed lines in the right panel corresponds to the frequency of the weak signal

Ω s i g / (2 π) =

1 Hz and its odd-order harmonics of 3 Hz and 5 Hz for guiding the eye. (b) The FFT spectra of the time trace results with the HF driving modulation strength

ω H F / (2 π) =

2.16 MHz, 2.52 MHz, 2.88 MHz, and 3.24 MHz under the condition of asymmetric bistable system, where

Δ a / (2 π) =

−0.3 MHz and the vertical dashed lines mean the frequencies of the two even harmonics at 2 Hz and 4 Hz. (c) Experimental SNR as the function of the HF driving for different symmetry of the bistable system with

Δ a / (2 π) =

0, −0.3 MHz, −0.6 MHz, −0.9 MHz, and −1.2 MHz. The stars correspond to the SNR for the FFT spectrum with the same color in Fig.2(b). The dashed line marks the corresponding

ω H F m a x

. The colored areas under the threshold

S N R T

= 3 dB indicate the weak LF signal indistinguishable from the noises. (d) Experimental observation and numerical simulation of SNR

m a x

as the function of

Δ a

. The shape of the experimental data matches the curves in Fig.2(c). Due to the symmetry of the effective bistable potential, we present only the results of

Δ a < 0

for simplicity.

Fig.3 The relaxed frequency separation condition. (a) The SNR of the output signal as a function of

ω H F

in variation with

Ω H F

in symmetric bistable system, where we set

Ω s i g / (2 π) =

1 Hz,

ω s i g / (2 π) =

0.72 MHz and the waveform of the HF driving as sinusoid. The dashed line marks the corresponding

ω H F m a x

; The colored areas under the threshold

S N R T =

3 dB indicate the weak LF signal indistinguishable from the noises. (b) The SNR

m a x

as the function of

Ω H F

Fig.4 Detection of a mixed signal and aperiodic signal using VR. (a) The FFT spectrum of a mixed signal under the condition of

ω 1 / (2 π) = ω 2 / (2 π) =

0.72 MHz,

Ω 1 / (2 π) =

1 Hz,

Ω 2 / (2 π) =

2.3 Hz,

ω H F / (2 π) =

4.32 MHz and

Ω H F / (2 π) =

100 Hz. The vertical dashed lines lie at the frequencies of the peaks marked as from A to G. (b) The input aperiodic signal (I) and the time trace of the photon counts under the condition of

ω H F / (2 π) =

0 (II), 1.44 MHz (III), 2.16 MHz (IV), 3.60 MHz (V) and 5.76 MHz (VI), where we set

ω a p / (2 π) =

0.72 MHz and

Ω H F / (2 π) =

100 Hz. In (I) the corresponding part of the input pattern of the weak binary aperiodic signal is shown with an arbitrary scale.

Fig.A1 Responses of different waveforms. SNR as a function of

ω H F

and the waveforms of the HF driving, where we set

Ω s i g / (2 π)

= 1 Hz and

ω s i g / (2 π) =

0.72 MHz, and

Ω H F / (2 π) =

100 Hz for periodic HF driving. For the HF driving with the waveform of white noise, we set the bandwidth to be 100 Hz.

Fig.A2 Experimental and numerical FFT spectra with

Ω H F / (2 π)

= 1.1 Hz. FFT spectra of the output signal in the condition of

Ω s i g / (2 π) =

1 Hz,

ω s i g / (2 π) =

0.72 MHz and

Ω H F / (2 π)

= 1.1 Hz,

ω H F / (2 π) =

2.16 MHz. The grey and yellow dashed lines locate at 1.0 Hz and 1.1 Hz, respectively.

Fig.A3 Responses of different

W b i

. SNR as a function of

ω H F

and the width of the bistability region

W b i

, where we set

Ω s i g / (2 π)

= 1 Hz,

ω s i g / (2 π) =

0.72 MHz and

Ω H F / (2 π) =

100 Hz. The weak signal is square-wave and the HF driving is sinusoidal wave.

W b i / (2 π)

is adjusted at 1.5 MHz, 3.0 MHz and 4.5 MHz.

Fig.A4 Responses of different amplitudes of the weak LF signal. SNR as a function of

ω H F

and the amplitudes of the weak LF signal

ω s i g

, where we set

Ω s i g / (2 π)

= 1 Hz and, and

Ω H F / (2 π) =

100 Hz. The

ω s i g

varies from 0.072 MHz to 1.440 MHz.

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