原子ニュートリノ観測のための 誘電体導波路中のqed...
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日本物理学会2016秋季大会 @ 宮崎大学木花キャンパス, 2016/9/22
田中 実阪大理
原子ニュートリノ観測のための誘電体導波路中のQED過程の解析
1
共同研究者: 笹尾 登(岡山大基礎研), 津村浩二(京大理),
吉村太彦(岡山大基礎研)
Minoru TANAKA 2
Radiative Emission of Neutrino Pair (RENP) A.Fukumi et al. PTEP (2012) 04D002; arXiv:1211.4904
Λ− |e⟩ → |g⟩ + γ + νiνj νi
|e⟩ → |g⟩ + γ + γ ×|p⟩
|e⟩ → |g⟩ + γ + νiνj
|e⟩ →|g⟩ + νiνj
|e⟩> 1
γ νi , i = 1, 2, 3
ωij =ϵeg
2− (mi + mj)2
2ϵeg.
ϵab = ϵa − ϵb |a⟩ , |b⟩mi
(mi + mj)2/(2ϵeg) ∼ 5 mi + mj = 0.1 ϵeg = 1
ω ≤ ω11
metastable
-
4.1560 4.1565 4.1570 4.15750.00
0.02
0.04
0.06
Ω !eV"Sp
ectru
mI#Ω$
Threshold behavior #Dirac case$
m0
132 136
2.5 × 1019 /cm3
1.1 × 1020 /cm3
> 1019 /cm3
∼ 102 s−1
1 × 104 s−1
O(0.1) µs
5p5(2P3/2)6p 6p
5p5(2P3/2)6p 2[3/2]2 5p5(2P3/2)6p 2[5/2]2
Λ6s [3/2]2 6s [3/2]1
6s [3/2]1
λtp λ6sJ−6p
A6sJ←6p
5p5(2P3/2)6p 2[3/2]2
Xe, Dirac, NH, IH
m0 = 2, 20, 50meV
valence spin current
D.N. Dinh, S.T. Petcov, N. Sasao, M.T., M. Yoshimura, PLB719(2013)154; arXiv:1209.4808
Rate enhancement by macrocoherence
Confirmed by PSR experiments1018 amplification
|p
|e
|g
Minoru TANAKA
QED backgrounds
3
|ei ! |gi+ + ijMacrocoherent amplification of RENP
Macrocoherent amplification of QED processesMcQ3|ei ! |gi+ 0 + 12
Ex. Xe
1 Introduction
With the advent of successful macro-coherent amplification (more than 1015) of QED rare processes [2],
namely the macro-coherent paired super-radiance (PSR) [3], the atomic project of neutrino mass spec-
troscopy [4] has gained a new stage of potentiality to explore important neutrino properties yet to be
measured and to ultimately detect the relic neutrino of temperature 1.9 K [5].
In the present work we address the problem of quantum electrodynamic (QED) backgrounds and propose
a scheme of QED background-free RENP (Radiative Emission of Neutrino Pair). Usual higher order QED
processes, when they occur spontaneously, are not at all serious backgrounds to macro-coherently amplified
atomic neutrino pair emission (RENP) if experiments of the neutrino mass spectroscopy are designed with a
repetition cycle sufficiently faster than the decay lifetime. (Even a repetition scheme slower than the decay
rate is conceivable if the dead time is not too large.) The macro-coherently amplified QED process may
however become a serious source of backgrounds, since their rates are much larger, as is made evident below.
We shall term macro-coherently amplified QED process of order n as McQn for brevity. The case of n = 2
corresponds to PSR. Since RENP process occurs with parity change, the main backgrounds are odd McQn.
Our proposal for the QED background rejection is to use either wave guides [6] or some type of pho-
tonic crystals [7] to host a target. A promising host is Bragg fiber consisting a hollow surrounded by two
periodically arranged dielectrics of a cylindrical shape [8], [9]. For brevity we call these hosts as host guides
in the present work. After we show below how QED backgrounds are rejected, we shall calculate spec-
tral rates of RENP (stimulated single photon emission) |e⟩ → |g⟩ + γ0 + νν in which no background of
McQ3 |e⟩ → |g⟩ + γ0 + γ1γ2 exists. Rejection of McQ5 and so on is then automatically guaranteed. The
background-free RENP rate is, to a good approximation, found to be a shifted (to the higher energy side)
spectrum in free space.
Parities of two states, |e⟩, |g⟩, for RENP are different. A good example of candidate de-excitation is from
the Xe excited state of JP = 1− of configuration 5p56s(8.437 eV) (the decay rate being ∼ 300 MHz) to the
ground state of 0+ of 5p6.
We show a part of Feynman diagrams (despite of the use of the non-relativistic perturbation theory
based on bound state electrons) in Fig(1). RENP diagrams are based on the nuclear monopole contribution
of [10]. Relevant Xe energy levels are shown in Fig(2).
! !!
e6s 6p 6s 5pA
!
e6s 7s 5p
""
Figure 1: A part of Feynman diagrams for Xe 3P1(8.437eV) RENP in the left and for McQ3 in the right.
Dashed red line in the left is for Coulomb excitation between nucleus A and a valence electron.
2
|ei |gi
M. Yoshimura, N. Sasao, MTPTEP (2015) 053B06; arXiv:15010571
serious BG though reducible
cf.
(McQ3) 1020 Hz
n
1020/cm3
3 V
cm3
3(t)
103
(RENP) 1 mHz
n
1020/cm3
3 V
cm3
!(t)
103
Minoru TANAKA
Radiation in waveguide/cavity
4
Purcell, Phys. Rev. 69, 681 (1964)
depends on environment
Emission rate (of single mode) / density of states
=P
PFSRatio of powers (classical)
Purcell factor
Fp :=
FS=
DoS
DoS in Free Space
(quantum)
Rate suppressionFp < 1
Minoru TANAKA
Band structure of photonic crystal
5
z
x
...... ......n1n2
a2a1
n1n2
a2a1
FieldE(x)ei(kz!t)
a = a1 + a2
TMTE
n1 = 4.6, n2 = 1.6, a2/a1 = 2
!a
ka-3 -2 -1 0 1 2 3
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Allowed bands of Bloch wave: TE left, TM right
E. Yablonovitch, PRL58, 2059 (1987)S. John, ibid., 2486 (1987)
band
cf. electronic band structure in solid
Periodic dielectric structuremanipulating photon propagation
complete Bragg reflectionWinn et al., Opt. Lett. 23, 1573 (1998)
Minoru TANAKA
Bragg fiber
6
Yeh, Yariv, Marom, J. Opt. Soc. Am. 68, 1196 (1977)Fink et al., J. Lightwave Technol. 17, 2039 (1999)
Similar band structureas the slab
!a
ka
n1 = 4.6, n2 = 1.6
Purcell factor
a2/a1 = 2, rc/(a1 + a2) = 2
Np = 5
hollow core fiber
Confinement of light by Bragg reflection
Minoru TANAKA
McQ3 rate in Bragg fiber
7
trigger|ei ! |gi+ 0(!0) + 1(!1) + 2(!2)
Rate suppression factor
rBF/FS(!0) :=1
FS(!0)
Zd!1
dFS
d!1Fp(!1, k1)Fp(!2, k2)
1 2 3 410-15
10-11
10-7
0.001
10.000
[eV]
Fp
Purcell factor (TM), Np=5,10,15
!max
= !eg/2 ' 4.22 eVn1 = 5.5, n2 = 1.3a = 0.126 µm, rc = 2a
6s 3P1 ! 5p 1S0Xe
a2a1
=
pn21 1p
n22 1
= 6.51
!0 = 0.95!eg/2
Minoru TANAKA 8
1 2 3 4
10-10
10-6
0.01
100
[eV]d
/d
Diff. rate, Np=0(FS),5,10,15
dFS
d!1Fp1Fp2
(4.8,1.3)
(5.5,1.6)
(5.5,1.3)
10 20 30 40 50 60 70
10-40
10-30
10-20
10-10
1
# of layer pairs
BF/
FS
Rate suppression factor
rBF/FS / exp(cNp)
Minoru TANAKA 9
Suppression of QED process in Bragg fiber
◼ Photonic crystal ~ periodic dielectric structure Band gap ~ vanishing DoS
◼ Purcell factor
Exponential rate suppression in the band gapfor large index contrast
Rate suppressionFp < 1
Fp = DoS/(DoS in free space)
forBF/FS 1025 n1 = 5.5, n2 = 1.3, Np = 40
◼ To do
Rate of McQ4 or higherIs necessary?n1 & 4.8 or 5.5
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