Application to microwave axion detectors .1 Introduction of microwave axion detector.1Introduction of microwave axion detector

PT-SYMMETRIC AMPLIFIER: BROADBAND SENSITIVITY IMPROVEMENT VIA COHERENT QUANTUM FEEDBACK

3.5 Application to microwave axion detectors .1 Introduction of microwave axion detector.1Introduction of microwave axion detector

The Sikivie Haloscope type axion detectors [19] we considered are designed to detect the weak conversion of dark matter axions into microwave photons in the presence of a strong magnetic field. For an axion detector consisting a station- ary magnetic field B₀ and a single mode ˆE𝑚 of a microwave resonator, it can be characterized by the following interaction Hamiltonian:

𝑉_axion =𝑔_{𝑎 𝛾 𝛾}A

∫

𝑑³xEˆ𝑚(x) ·B₀(x), (3.32) where 𝑔_{𝑎 𝛾 𝛾} is axion-photon-photon coupling constant, A is the axion field (with negligible spatial variation), and ˆE𝑚(x) = E𝑚(x) (𝑎ˆ+ 𝑎ˆ^†)/√

2 is the electric field operator of the microwave mode, with (𝑎,ˆ 𝑎ˆ^†) being the annihilation and creation operators, and the mode functionE𝑚(x) satisfying∫

E²𝑚(x)𝑑³x =4𝜋~𝜔₀, with𝜔₀ being eigenfrequency of the mode.

Using𝜔₀as carrier frequency, we can rewrite Eq. (3.32) as:

𝑉_axion=𝛼_axion(Ψ₁𝑎ˆ₁+Ψ₂𝑎ˆ₂). (3.33) Here ˆ𝑎₁_,₂are the mode quadratures of the electric field, Ψ₁ = (Ψ+Ψ^∗)/√

2, Ψ₂ = (Ψ−Ψ^∗)/(√

2𝑖) are two quadratures of the oscillations of the axion field, A (𝑡) = Ψ(𝑡)𝑒⁻^𝑖𝜔⁰^𝑡+Ψ^∗(𝑡)𝑒^𝑖𝜔⁰^𝑡. The coupling coefficient are defined as:

𝛼_axion ≡4𝜋𝜂𝑔_{𝑎 𝛾 𝛾} p

~𝜔₀E𝐵, (3.34)

where E𝐵 is the energy of magnetic field, and 𝜂 is the overlap between the static magnetic field and the cavity mode:

𝜂 =

∫

E𝑚(x) ·B₀(x)𝑑³x . h∫

|E²𝑚|𝑑³x·

∫

|B²₀|𝑑³x i1/2

. (3.35) Note that𝜔₀is the central frequency at which the device operates, and it needs to be scanned over different values to search for the yet unknown Compton frequency of axion.

We then discuss the figure of merit for axion searches [56, 57] — the effective scan rate. As shown in Fig. 3.7, the broadband search for axion’s Compton frequency requires many different such data stretches with duration𝑇 = Γ⁻¹

𝐴 , possibly using different detector configurations. Let us divide the entire bandwidth of Γ into

/()

Γ (Search Bandwidth)

1 2

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Figure 3.7: Illustration of the axion search. The entire bandwidth Γ is divided into bins with widthΓ𝐴, and to be covered by a (large) number of detectors (three shown in the figure, in terms of their 1/𝑆_Ψ(Ω)). Each bin can get contribution from multiple detectors; for example, the highlighted bin is covered by both detectors 1 and 2.

discrete angular frequencies separated byΓ𝐴, which we label asΔ𝑗, 𝑗 =1,2, . . . , 𝑛, with

𝑛= Γ/Γ𝐴. (3.36)

We shall approximately view the search as to be carried out independently for each of these bins.

Our requirement is that for the same fiducial axion amplitude 𝐴₀(eventually the minimum detectable axion-field amplitude), we can cumulate at least 𝜌²

th for each axion frequency bin. Note that to achieve the same statistical significance,𝜌²

thshould increase as the number of bins (hence the independent trials) increase, but rather mildly. Let us make a very crude estimation. Regarding our problem as having 𝑛 = Γ/Γ𝐴 independent trials, an overall false-alarm probability of 𝜖 requires each bin to have

𝑝_FA =𝜖/𝑁 =𝜖 𝛾_𝑎/Γ. (3.37)

In absence of axion field, in the ideal situation, each 𝜌 satisfies an exponential distribution, which means

𝜌²

th ∼ |log(𝜖 𝛾_𝑎/Γ) |, (3.38) which indeed depends very mildly on the number of bins.

For each run, let us assume that we have a noise spectrum of 𝑆_𝐽(Ω). For bin 𝑗, we perform

𝑍⁽

𝑗)

𝐽 =

∫ ^𝑇

𝑧⁽

𝑗)

𝐽 (𝑡)cosΔ𝑗𝑡 𝑑 𝑡

∫ ^𝑇

𝑧⁽

𝑗)

𝐽 (𝑡)sinΔ𝑗𝑡 𝑑 𝑡

. (3.39)

Here 𝑧⁽^𝑗)

𝐽 (𝑡) = 𝑛_𝐽(𝑡) + 𝐴₀cos(Δ𝑗𝑡+ 𝜙₀) where the second term is a fiducial axion term with amplitud 𝐴₀ and unknown phase 𝜙₀. Thus we have (up to numerical factors):

h𝑍⁽

𝑗) 𝐽 i= 𝐴²

0𝑇²+𝑆_𝐽(Δ𝑗)𝑇 , Var𝑍⁽^𝑗) =𝑆²

𝐽(Δ𝑗)𝑇². (3.40) It is the 𝐴₀contribution to the expectation of𝑍⁽^𝑗)

𝐽 that we are aiming to detect. We do this by combining multiple observations. If we assign coefficient𝑐⁽^𝑗)

𝐽 for the 𝐽 observation, we will obtain

𝑐⁽^𝑗)

𝐽 ∝ 1

𝑆²

𝐽(Δ𝑗)

, (3.41)

and the total SNR squared we get for the 𝑗-th bin is given by 𝜌⁽^𝑗)2

=Õ

𝐽

𝐴⁴

0𝑇² 𝑆²

𝐽(Δ𝑗)

. (3.42)

If we focus on each detector 𝐽, the figure of merit for axion detection should be counted by the integral of total SNR squared:

∫ 1

𝑆²(Ω)𝑑Ω, (3.43)

which is called theeffective scan rate. We will use that to optimize the amplifier for axion detection in the following section.

3.5.2 PT-symmetric amplifier for axion detection

The circuit diagram that can realize Hamiltonian (3.2) for axion detection is shown in Fig. 3.8a. The parametric amplification can be realized by a 3-wave mix- ing device [58–60]; sWLC corresponds to having ˆ𝑏 mode coupled to the external continuum (“sWLC readout” in the figure), while uWLC corresponds to having ˆ𝑎 mode coupled to the external continuum (“conventional/uWLC readout” in the figure). For conventional readout with𝜅=0, the circuit is reduced to be a conventional detector.

Bode plots of the signal transfer function, i.e., from Ψ to ˆ𝑣, in sWLC and conventional schemes are shown in Fig. 3.8 b. From the feedback control viewpoint discussed in Sec. 3.3 and in Fig. 3.4, the 𝜒 = 0 lines represent the open-loop signal transfer function of sWLC, while the 𝜒/𝜅 =0.995,1,1.005 lines represent the closed-loop ones. Note that the system is unstable for 𝜒/𝜅 = 1.005 > 1, shown by the light blue lines, where the phase of signal transfer function decreases with frequency around the resonance near DC, which is different from the red lines with monotonically increasing phases.

- -

()

=

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/= 0.995

<latexit sha1_base64="RnHpYhJY9XgTBbRa4NljaTizDCc=">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</latexit><latexit sha1_base64="RnHpYhJY9XgTBbRa4NljaTizDCc=">AAACn3icdVFNbxMxEHW2fJTwlcCRiyGqxCm7m4amRUKq4AAnFCTSFiWryOtMNtZ6bcuebRWt8lO4wm/i3+BNAiIRHcny03vzZuyZ1EjhMIp+NYKDO3fv3T980Hz46PGTp632swunS8thxLXU9iplDqRQMEKBEq6MBVakEi7T/EOtX16DdUKrr7g0kBQsU2IuOENPTVvtCV+IcJIzY9i7qHt29mba6vj79KTXP6FRN4oGcS+uQW/QP+7T2DN1dMg2htN243oy07wsQCGXzLlxHBlMKmZRcAmr5qR0YBjPWQZjDxUrwCXV+u0reuSZGZ1r649Cumb/dVSscG5ZpD6zYLhw+1pN/k8blzg/TSqhTImg+KbRvJQUNa0HQWfCAke59IBxK/xbKV8wyzj6ce1UStPMAuQyqeouaarlar+Y52Z0nUUl4H6Fv384ogtE8zYMOTLV1TYLTZ6FW3XHYUQ9jlsMG7HpN/VnHfR2cNHrxh5/6XfO3293dkhekFfkNYnJgJyTT2RIRoSTG/Kd/CA/g5fBx+BzMNykBo2t5znZieDbb+sEzwM=</latexit><latexit sha1_base64="RnHpYhJY9XgTBbRa4NljaTizDCc=">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</latexit><latexit sha1_base64="RnHpYhJY9XgTBbRa4NljaTizDCc=">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</latexit>

= 0

<latexit sha1_base64="6AwBkEiAXNWiT9rFnPQI45Ar66k=">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</latexit><latexit sha1_base64="6AwBkEiAXNWiT9rFnPQI45Ar66k=">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</latexit><latexit sha1_base64="6AwBkEiAXNWiT9rFnPQI45Ar66k=">AAACknicdVHLahsxFJUnfSTuK2mzy0bUBLqyZ1wTp4FA2myyyCKF2gnYQ5Dk67FqjSSkOwEz+B+6bf+sf1ON7YTYNBcEh3PuuQ9dbpX0GMd/a9HWs+cvXm7v1F+9fvP23e7e+743hRPQE0YZd8OZByU19FCighvrgOVcwTWfnlf69R04L43+gTMLac4yLcdSMAxUfygm8jS+3W3EzS/HR+3OEY2bcdxN2kkF2t3O5w5NAlNFg6zi6navdjccGVHkoFEo5v0giS2mJXMohYJ5fVh4sExMWQaDADXLwaflYtw5PQzMiI6NC08jXbCPHSXLvZ/lPGTmDCd+U6vI/2mDAsfHaSm1LRC0WDYaF4qiodXudCQdCFSzAJhwMsxKxYQ5JjD80FolzjMHMFVpWXXh3Kj5ZrHAjegiiyrAzQoPOxzSCaI9abUEMt00LmvZadZaqWsOK6vveMKwFOvhUvfnoE+DfruZBPy90zj7trrZNjkgH8knkpAuOSMX5Ir0iCA/yS/ym/yJ9qOT6Gt0vkyNaivPB7IW0eU/L63K9w==</latexit><latexit sha1_base64="6AwBkEiAXNWiT9rFnPQI45Ar66k=">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</latexit>

conventional

<latexit sha1_base64="qZgxI3ri83DP7sYwbWUQ+gEhFD8=">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</latexit><latexit sha1_base64="qZgxI3ri83DP7sYwbWUQ+gEhFD8=">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</latexit><latexit sha1_base64="qZgxI3ri83DP7sYwbWUQ+gEhFD8=">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</latexit><latexit sha1_base64="qZgxI3ri83DP7sYwbWUQ+gEhFD8=">AAACnnicdVHBahsxEJW3bZK6beo0x15ETaAne7cEUnIKCZReShKIHYO9GEker4W1kpBmDWbxn+Sa/lP/plp7KbXdDgge7828Gc1wq6THOP7ViF68fHVwePS6+ebtu+P3rZMPfW8KJ6AnjDJuwJkHJTX0UKKCgXXAcq7gkc9vKv1xAc5Lox9waSHNWablVAqGgRq3WiOXU2H0AnRFMDVuteNOvA66D5IatEkdd+OTxmI0MaLIg4NQzPthEltMS+ZQCgWr5qjwYJmYswyGAWqWg0/L9egrehaYCZ0aF55Gumb/rihZ7v0y5yEzZzjzu1pF/ksbFjj9mpZS2wJBi02jaaEoGlrtgU6kA4FqGQATToZZqZgxxwSGbW05cZ45gLlKy6oL50atds0CN6HrLKoAdx3+/OGMzhDtZbcrkOmOcVnXzrNurW5VWFmt4z8FG7EZLpXs3mUf9L90koDvz9tX1/XNjshH8ol8Jgm5IFfkO7kjPSLIgjyRZ/IzotG36Ed0u0mNGnXNKdmKaPAbZDbPuA==</latexit>

=

/= 0.995

= 0

conventional

/= 1.005

Φ(t)

a , a

^†

b , b

^†

c , c

^†

signal

ˆ

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ˆ



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a sWLC readout conventional/uWLC readout

Figure 3.8: Microwave axion detector and the Bode plots for signal transfer functions. a, Circuit diagram of an axion detector (dashed box on the right) attached to a quantum amplifier (dashed box on the left). The parametric amplifier is achieved by Josephson 3-wave mixer indicated by the×symbol in the figure, with Φ(𝑡) indicating time-depending external flux that act as parametric pumping (see Figure 9 of Ref. [59]). Coupling “sWLC readout” to a continuum results in a sWLC, while keeping “conventional/uWLC readout” coupling to a continuum results in uWLC, and for comparison, using “conventional/uWLC readout” without coupling to “quantum amplifier” results in a conventional detector. b, Bode plot of the transfer function from “signal” to “sWLC readout” with 𝜅 = 10𝛾_𝑅 and 𝛾_𝐿 = 0 (lossless), with the black lines representing signal transfer function of conventional detector for comparison. Note that the light blue lines represent an unstable parameter setting in sWLC scheme.

Dalam dokumen for Detector Improvement and High-Precision Modeling of Binary Black Hole Ringdown Waveform (Halaman 90-94)