PT-SYMMETRIC AMPLIFIER: BROADBAND SENSITIVITY IMPROVEMENT VIA COHERENT QUANTUM FEEDBACK
3.6 Discussion
We proposed a quantum amplifier that can be attached to an existing sensor as a coherent quantum feedback device, and improve its sensitivity-bandwidth product.
The improvement is achieved via signal amplification, and therefore, is robust against readout losses. The sensitivity gain has an interesting connection toPT-symmetry:
a mode ˆ𝑏 is coupled to the original sensor modes{𝑎ˆ𝑗}, as well as auxiliary modes {𝑐ˆ𝑗}, which is time reversal to {𝑎ˆ𝑗}; furthermore, the readout is carried out from mode ˆ𝑏 which is the only one that couples to the continuum, and thus, coherent noise cancellation is achieved when the couplings to original and auxiliary modes match. Such a strategy can be used to substantially improve the sensitivity of laser interferometer gravitational-wave detectors and microwave axion detectors. We analyzed different figures of merit, Eqs. (3.8) and (3.44), for the two detector schemes
SC, vacuum
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0.1 1 10 100 1000
0.1 1 10 100 1000
/ L
S2 sWLC with / L=500, sqdB=0
sWLC with / L=500, sqdB=10 SC with sqdB=0
SC with sqdB=10 / L= 500,sqz 10dB
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/ L= 500,vacuum
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SC, sqz 10d B
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10
20 30
40 50
10 20
30 40
0 2 4 6 8 10 12 14
0 200 400 600 800 1000
Squeezing factor(dB) /L
10
20 30
40 50
10 20
30 40
0 2 4 6 8 10 12 14
0 200 400 600 800 1000
Squeezing factor(dB) /L
0.1 1 10 100 1000
0.1 1 10 100 1000
/ L
S2 sWLC with / L=500, sqdB=0
sWLC with / L=500, sqdB=10 SC with sqdB=0
SC with sqdB=10
0.1 1 10 100 1000
0.1 1 10 100 1000
/ L
S2 sWLC with / L=500, sqdB=0
sWLC with / L=500, sqdB=10 SC with sqdB=0
SC with sqdB=10 a
b
Figure 3.9: Sensitivity improvement for axion detection. a, The enhancement of effective scan rateR𝑎achievable by sWLC (black solid lines) and uWLC (red dashed lines) axion detectors over the single-cavity one, as a function of the amplifier gain 𝜒 and squeezing factor𝑒−2𝑟, optimized over the rate of ˆ𝑎- ˆ𝑏 coupling𝜅 and readout coupling 𝛾𝑅. b, Examples of single-cavity (SC) and sWLC noise spectrum with R𝑎-optimized𝜅, 𝛾𝑅 for different 𝜒and input squeezing levels (sqz)𝑒−2𝑟 shown by color dots ina. Note that all couplings are shown in the unit of the generic loss rate 𝛾𝐿.
respectively. Furthermore, in optomechanical GW detection, a more completePT- symmetric structure for back-action evasion is proposed using fictitious negative resonance. We leave the more detailed study to future work.
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