Understanding and reducing
electromagnetic heat transfer
Carsten Henkel
META’15 session ‘Thermoplasmonics and near-field ...’ (NYC August 2015)
merci à :
G. Barton (Sussex, UK), V. E. Mkrtchian (Ashtarak, ARM), DFG (e ‘IANV hybrids’)
details in:
‘Friction forces on atoms after acceleration’
F. Intravaia & al, J Phys Cond Matt 27 (2015) 214020
Institute of Physics and Astronomy, Universität Potsdam, Germany
www.quantum.physik.uni-potsdam.de
download slides
Abstract key words
small particles as second thermal contact
– settings: atom chips, ion traps
– goal: reduce thermal contact (already weak ...)
lower magnetic noise
– metal strips (biomagnetism expts)
– work on alloys (Ron) and semiconductors (Harald)
– outline numerical method
quantum friction: “elementary processes”
– also: e-ifm and path decoherence
(Scheel & Buhmann, Phys Rev A 2012)
– low-v behaviour
– local thermal equilibrium: is it valid? what does it mean?
New York Aug 2015
weburbanist.com (2013)
Understanding and reducing . . .
“Curved skyscraper melts cars, starts fires with heat of Sun”
New York Aug 2015
Understanding and reducing . . .
• Basic mechanisms:
emission T1 & absorption T2
frequency spectra
dilute one medium
→ elementary emitter / absorber
T2
d
F~v
0←
T
v
T1
driven by temperature difference
by relative motion: friction
New York Aug 2015
Understanding heat transfer with small probes
electric noise (trapped ultracold ions)
Brownnutt & Blatt group (arXiv 2014)
Varpula & Poutanen (J Appl Phys 1984)
magnetic noise spectrum
Rytov theory
1/d4 slope – ‘patch charges’, ‘adsorbates’ ?
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Noise reduction strategies
What for?
• biomagnetic imaging (improve S/N)
• long-lived microtraps (‘atom chips’, ‘ion chips’) ← IANV ‘Hybrid systems’ project
• ion-based quantum computing (Blatt/Innsbruck, Wineland/NIST)
New York Aug 2015
Noise reduction strategies
Example: magnetic noise
TABLE II. Thermal noise measured from a 32325 cm2 aluminum foil
~t512 mm! sliced into electrically isolated strips of the width D ~cm!. Measured noise levels B mn,z are given in fT/AHz, and B ref
n,z is the measured value
of the unsliced foil. Gradiometer location was either at the center of the strip
~uou! or above a cut ~o” !.
D
Location
B mn,z
B mn,z /B ref
n,z
32
16
8
8
4
4
2
1
uou
o”
uou
o”
uou
o”
uou, o”
uou, o”
13.7
6.8
12.3
6.4
8.9
6.3
4.7
2.7
1.00
0.49
0.90
0.47
0.64
0.46
0.34
0.20
instrumental noise of a first-order axial dc-SQUID
81 mm, pickup coil diameter 38 mm! inside the Othielded room. Ten NRC2-superinsulation layers were
The noise spectrum of the same system, when the
patches.&c!Katila,
Mea- ‘Thermal noise in biomagnetic measurements’ (Rev Sci Instr 1996) 2
were constructed 131
cm2 isolated
Nenonen,
Montonen
from 13.7 fT/AHz ~unsliced foil! to 2.7 fT/AHz ~1325 cm
ental noise when the gradiometer was mounted inside
ld.
strips!.
about 1.9 fT/AHz, we obtain an estimate of
he instrumental noise, which agrees well
result of Fig. 8~a!.
inum foils, our Dewar contains a vapor-
We also tested the influence of striping when a 12 m m
thick aluminum foil ~32325 cm2 ) was wrapped around the
measurement Dewar. The measured noise in the case of a
continuous foil was 13.0 fT/AHz. After slicing the foil into
New York Aug 2015
2, 4, and 32 strips, the measured noise was reduced, corre-
Noise reduction strategies
330
atom trap
quasi-1D
(20)
me form as the result for the
here the tensor Ỹij holds the
alloy Ag:Au
Rapide Not
ps
10 x 2 µm
Highlight Paper
kB T
σxx Ỹij .
4π 2 ϵ20 c4
height 5 µm
discuss the current flow in imperfec
a spatially modulated conductivity a
Wire material
Large wire
Smal
malism developed in references [34,3
Central part Legs γspin decoherence γspin de
case.
Au
Au
1
Au
3.68 × 10−4
SrNbOI
SrNbOII
Au
4.39 × 10−4
3.1
System
definition
HOPG
Au
9.7 × 10−3
1
9.9 ×
1×
1.8 ×
We now consider a thin metal wire w
tuations,
as sketched in
in Table
Figure2.3.Ob
T
The results
are summarized
4.3 Contribution from structures providing longitudinal would be preferable
is again defined
such
that
the
wire
le
to have the entire wire ma
confinement
direction,
its
width
W
along
ŷ,
and
anisotropic
Fig. 2. (Color online) Lines: spin decoherence
rate materials. However, for that the orie
ẑ. The
crystal used
for t
the
crystalline
axis anisotropic
in the area forming
the ‘legs’
γspin decoherence as a function of electrical anisotropy r =
assumed
to
be
‘aligned’
with
the
w
ofThe
cold
atoms
with
anisotropic
conductors’
(Eur
Phys
J
D
2008)
perpendicular
to
the
central
part
of
the
z-wire,
most common
magnetic
micro-trap
σxx /σyy , Ioffe-Pritchard
for layered and quasi-1D
conducting
materials. Wire
tion
(10).
This
is
of
course
not
the
m
configurationparameters
is that of were
a z-shaped
wireWcombined
d = 5 µm,
= 10 µm,with
H =an2.15fabrication
µm, and complexity. However, having the ‘l
however
it
is
sufficient
for
our
purpo
a good
normal metal, with isotropic conductivity,
temperature
of Tpart
= 300
K. wire
For these
lines,ofthe
external biassurface
field [1].
The central
of the
creates
the
fabrication,
lowers power consumption and
conductivity
along
the wire
was assumed
to be identical to that
a guide potential,
while the
‘legs’
provide
the longitudinal
ing.
Indeed
we
find that even if the metal ‘le
materials
having
conducting axis
confinement ofasAu.
wellFor
as layered
the non-zero
field
valuethe
at badly
the trap
3.2
Current
corrugations
the wireinthickness
red), magnetic
only a slightanisotropic
improve- material reach
up to the central p
minimum, asalong
illustrated
Figure 6.(dashed
In realistic
ment
is
gained,
and
the
dependence
on
the
anisotropy
is
neglitrapping
wire,
the
reduction
of the the decohe
micro-traps, where longitudinal-confinement is required,
gible.
If
the
badly
conducting
axis
is
along
the
width
of
the
wire
In
the
isotropic
case
[34,36] we start
is
still
significant.
considering only the potential generated by the central
(dashed-dotted
blue),
the
improvement
is
more
pronounced,
part of the z-wire does not suffice for the anisotropic case,
but still saturates at relatively low anisotropy. For quasi-1D New York Aug 2015
E = ρJ,
as the contribution
from the ‘legs’ of the z-wire has to be
materials (dotted green - quasi-1D with both low conductivity
taken into account. This is expected to be more and more 5 Conclusions
terms of the same order; solid black - the more extreme case where ρ = σ −1 = ρ0 +δρ is the scalar
Rapide Not
Highlight
see that Bxx can be considtwo badly conducting axes,
than σxx . This does not lead,
he spin flip rate, as the Bxx
ization axis.
Fig. 1. (Color online) Improved trap lifetime upon cooling of
r components, Byy and Bzz ,
the surface. Comparison of a standard Au wire (dashed blue)
the
ghly conducting σxx andDavid
&wires
Folman
interactions
with
of similargroup,
geometry‘Magnetic
made of an Ag:Au
alloy (dashedgeometrical factors Xij have dotted red) [23] and the quasi-1D SrNbO
3.41 (solid black). The
Appendix A in [23]) for the long lifetime for the anisotropic wire at room temperature is
rom this analysis it emerges due to its rather high residual (low-temperature) resistivity
geometry, all of the non-zero even along its best axis (oriented along the wire). See Secorder. Thus the main differ- tion 4.2 for the implications of highly resistive wires in realists is due to the difference in tic experiments. No limiting lifetime level due to collisions with
onductivity σxx is dominant. background gas atoms is included. Losses due to this process
ent to the trap lifetime using are expected to be less significant in cryogenic experiments
m temperature is expected to as typically the background pressure is such experiments is
smaller. Wire dimensions are: width W = 10 µm, thickness
∼ 2.
The conclusion here is that although electrically
anisotropic materials are promising candidates for reducing the coupling of noise to the atoms, their advantages
are limited to moderate current densities. This should not
pose overly stringent restrictions on possible applications,
as at small atom-surface distances the required currents
for small and tight traps are not very high.
hlight Paper
re low, the high temperature
is applicable, and thus the
ctrum approaches
325
Table 2. The affect of longitudinal confinement on
tion of the decoherence-rate when using electrically
materials. Two z-shaped wire geometries, as illustra
ure 6, are considered: a large wire (d = 50 µm, W
H = 1 µm, Lcentral = 1 mm, and Llegs = 1.5 mm), a
wire (d = 3 µm, W = 6 µm, H = 1 µm, Lcentral
Llegs = 30 µm). The good conductivity axis (t
is along the central part of the wire. The spin d
rate, normalized to that of a structure entirely m
is calculated for different combinations of wire ma
positions.Physical
The externally
applied current density
326
The European
Journal D
2
9
3.3
×
10
A/m
and
8.5
×
109 A/m2 for the large
Fig. 6. (Color online) Schematic illustration of the studied
z-shaped wires. The atoms are trapped at a distance d from wires, respectively, such that the heating of the wire
◦
independent
spatial
C Time
(see Sect.
4.2). The difference
betwec
the central part of the wire of length Lcentral , made of an exceed 100 3
300
K
5
µm
for the
SrNbO
the worst co
anisotropic material as summarized in Table 2. This part of the calculations of
3.41 is whether
magnetic
potential
wire provides the radial trapping potential. The longitudinal axis of this quasi-1D material is along the wire width
(SrNbOII).materials
Even for small
confinement is provided by the z-wire ‘legs’ of length Llegs , or its thickness
Anisotropic
affectstructure
not onl
close
to
the
trapping
area
over pertu
the c
made of Au. The width W and thickness H are the same for Au ‘legs’ very
leading to the time-dependent
of the z-wire,far,
thebut
suppression
of
the
decoherence
the whole wire.
also the static corrugationa
rates is still tential
significant,
showing
the appe
thatfurther
fragment
an atom
clou
electrically anisotropic materials for realistic tight t
Note
Proposal for atom traps
– cooling
– alloys
– anisotropic conductors
d et al.: Magnetic interactions of cold atoms with anisotropic conductors
The European Physical Journal D
Noise reduction: semiconductors
Page 3 of 12
ster equa-
state, the
tion of the
s in equauclear spin
vel system
or a static
an angle θ
magnetic
loss rate % !s#1 #
pped (not
tom chip,
magnetic
frequency.
magneton
spectrum
er second.
r conduct[33,50,51].
f trapped
d setting a
ps [27,28].
g material
Local
Au
103
1
z
Nonlocal
"
10#3
10#4
ln!2z"!#
!
10#2
(a)
z#4
#1
n-Si
∆
1
102
distance z !Μm#
10#5
106
scaling law of magnetic field spectrum at low frequencies
loss rate % !s#1 #
(4)
106
10#4
103
1
Γ"Ω p ( 0.005
hBi (r, t0 )B
j (r, t)iω ≈
"
!
!
µ20 kB T σ
32π
∆ !∆
δij + ẑi ẑj
,
z
∆
`zδ=
r
2
µ0 ωσ
Haakh &
CH, ‘Magnetic near fields as a probe of charge transport in spatially dispersive conductors’
#3
10
10#4
10#2
(Eur Phys
J B 2012)
(b)
1
distance z !Μm#
102
Fig. 2. (a) Spin flip (loss) rate near a conducting halfspace described by the nonlocal Boltzmann-Mermin conductivity (8)−(11). The local description (Drude conductivity (12))
and the asymptotic expressions of equation (6) (dashed) are
shown for comparison. The length scales Λ = vF /ωp , ℓ = vF /γ,
and δ (Eq. (7)) illustrate the Thomas-Fermi screening length,
the mean free path, and the skin depth. The parameters are
New York Aug 2015
07-8
‘Full’ numerics
084907-2
J. Appl. Phys. 102, 084907 #2007$
B. Zhang and C. Henkel
Equilibrium near field correlations
trum and discuss the accuracy of the surface impedance approximation. Section IV is devoted to our numerical scheme
B
0
and to the results for single and multiple objects
of rectanij
j
ω
gular shape.
hBi (r0 , t0 )B (r, t)i ≈
2k T
Im G (r , r; ω)
ω
– radiation of magnetic
dipole µ NOISE
II. MAGNETIC NEAR-FIELD
A. Local
noise power
– object
surface:
boundary
conditions
B. Zhang and
C. Henkel
The fluctuations of the thermal magnetic field B!r , t" are
characterized by their local power spectral density !the Fourier transform of the autocorrelation function",
Bij!r; !" =
#
d"ei!"$Bi!r,t"B j!r,t + ""%.
J. Appl. Phys. 102, 084907 !2007"
FIG. 1. Sketch of the considered geometry: !left" current fluctuations in a
microstructure generate magnetic field fluctuations B!r!" at a position r!
outside it. !right" The magnetic noise spectrum is calculated from the magnetic field radiated by a point magnetic dipole ! located at r!. D and D!:
domains where the conductivity )!r ; !" is nonzero or zero, respectively.
!1"
benefit of this formula is that it holds also for the full correlation tensor and even near material objects that absorb the
field or generate thermal radiation. Generalizations to the
nonequilibrium case exist !fields produced by a “hot object”
surrounded by a “cold” environment",19,20,35,36 but are not
needed for our purposes !see the remarks in Sec. V". We also
note that the temperature-dependent prefactor in Eq. !3" reduces to 2kBT / ! for T + 0.1 K. In this limit, the order of
field operators in the correlation function Eq. !1" becomes
irrelevant. !The order we have adopted yields the rate of a
magnetic dipole transition i → f with energy difference E f
− Ei = *!."
Higher moments are not needed for our purposes, and the
average field !at frequency !" vanishes as is typical for thermal radiation. We assume the field to be statistically stationary so that the spectrum Eq. !1" does not depend on t. The
diagonal tensor components Bii!r ; !" give the spectrum for a
given Cartesian component Bi!r" or polarization direction.
Previous work has shown a strong dependence on the position r near a metallic microstructure, power laws being the
typical behavior in the frequency range where the wavelength # = 2$c / ! is much larger than the typical distances.
For the temperature dependence, see Eq. !3" below. Our parameters of interest are: normal metallic conductors with
temperatures above a few Kelvin, r in the micron range and
B. Magnetic dipole radiation
# of the order of centimeters or larger !! / 2$ % 10 GHz".
8. !Color online" Noise power generated
three
as a corresponds
function toofthedistance
!see inset
line electrodynamic
illustrating the observation
Thisby
upper
limitwires,
on frequency
strong magWesketch,
are thus with
led to the
solvedashed
the following
& CH,
noise
metallic
microstructures’
Appl
Phys
2007)
netic dipole
transitions
typical
atoms.
Inby
thisaregime,
". The wires have aZhang
quadratic
cross‘Magnetic
section
20"
20 around
#m inand
arealkali
separated
gap of (J
20
#m. The
is measured
above
center of the central
problem:
find noise
the
complex
magnetic
field the
amplitude
thepanel:
frequency
dependence
of the noise spectrum
is weak
and
by a incoherent
monochromaticsummation.
point dipole !For
!t" comparison, a
B!r
; ! * !" created
Left panel: horizontal polarization, right
vertical
polarization.
Symbols:
numerical
result;
solid line:
−i!t
occurs via the material response &permittivity &!!"'. A char= !e + c.c. located at position r!. We then compute
#mpenetration
" 80 #mlength
with!skin
approximately
the same volume !dash-dotted line" are shown. Skin
wire of same cross section !dashed line"
and alength
widescale
wire
20 field
acteristic
is the
! Bi!r; !*!"
! = 70 #m.
depth" ' defined by
.
!4"
Gij!r,r! ; !" =
!(j
New York Aug 2015
1 2$
!2"
=
Im(&!!" = ( 21 (0!)!!",
In the limit r → r! this field becomes the singular “self-field”
' #
Understanding fundamentals: friction forces
F~v
excitations (photons . . . ) leave the system
& energy conservation
– internal energy (“heat”)
– open boundaries
friction force vs power:
0←
T
delay between particle
and image dipole (surface charge)
• lateral force
zero friction above perfect conductor
F(v) · v + P (v) = 0
F~v
Discussion in the Literature
Ferrell & Ritchie 1980
Schaich & Harris 1981
Persson (& Volokitin) 1982...
Levitov 1989
Liebsch 1997
Despoja, Echenique,
& Šunjić 2011
Teodorovich 1978
Polevoi 1990
Barton 1996...
Pendry 1998
Dedkov & Kyasov 1999...
Dorofeyev 1999...
Philbin & Leonhardt 2009...
Silveirinha 2013...
matter excitations
(electron-hole pairs ...)
carrier scattering
e.m. excitations
(plasmon-polaritons)
macroscopic QED
Volokitin & Persson (RMP 2007)
Fulling & Davies 1976
Unruh 1976
Barton 1991...
Braginsky & Khalili 1991...
Høye & Brevik 1992...
Jaekel & Reynaud 1992...
Maia Neto & Reynaud 1993...
Dodonov 2001 ...
Bei-Lok Hu & al 2003...
Passante & al 2007...
macroscopic objects
moving boundaries
scalar fields
Kardar & Golestanian (RMP 1999)
Buhmann (Springer 2012/13)
Barton’s minimal quantum field theory
Barton (New J Phys 12 (2010) 113045)
Atomic levels |gi, |xi, |yi, |zi, EA = 0, h̄Ω
| {z }
|~η i or |ei
one-‘photon’ states |κi = |k, ωi
electric potential
Z
φ(~r(t)) = dκ φκ eik·r(t) e−kz aκ e−iωt + h.c.
g Κ1 Κ2
eΚ
gΚ
spectral density of surface plasmon polaritons
e vac
spectral density
Barton (1970s ... New J Phys 2010)
g vac
ω / Ωp
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
"
ΩS
0.2
0.4
0.6
0.8
1
1.2
K c / Ωp
Relevant time scales
−∞ . . .
couple field + atom at rest
...
acceleration time τ = “launch”
Barton: τ = 0 ‘instantaneous’
surface response 1/ωS , 1/Γ = “image delay”
...
atomic lifetime 1/γe = “resonant decay”
...
quasi-stationary state
spontaneous excitation 1/γg = “Cherenkov process”
One-photon Cherenkov process
dressed ground state (incl Lamb shift)
|Gi ≈ e−iδEg t |g vaci +
Doppler shifted resonance k ≥
Ω+ω
v
Z
dκ
heκ|V |g vaci
|eκi + . . .
Ω + ω − kv − i0
lifetime exponentially long
γg = −2 Im δEg ∝ exp[−(Ω + ωS )z/v]
1
Γg Γe
0.01
x z
0.0001
y
1. ´ 10-6
vWz
0
0.1
0.2
0.3
0.4
0.5
0.6
excitation g → e with 2 = 1 +h̄Ω
“for free” since Ω + ω 0 = 0
Barton’s
transient = excitation after launch
Barton’s transient = excitation after launch
vHtL
excitation probability
• virtual (“dressed |gi”) + real excitation (“bare |ei”)
v!t"
• virtual (“dressed |gi”) + real excitation
Z
(1)
(3)
pe (t) = d |c1 (t) + c1 (t)|2 → pe (real)
pe HtL
pe !t"
-1
0
1
2
3
t
three launches: “kick-start” vs “smooth”
!1
0
1
2
3
t
for τ t 1/γe
excitation ∝ v 2 f (τ ) acceleration spectrum
Barton & Calogeracos (J Phys A 2008)
Passante & co-w (Phys Lett A 1983...)
spontaneous decay relevant for
power balance
Psp ∼ −h̄(Ω + ωS )pe (real)γe
∝ −v 2
• compensates linear friction 6= Barton 2010
Review of Barton’s Results
Two-photon power g → g + hν1 + hν2
not the standard theory
Z
d
P2 =
dκ1 dκ2 h̄(ω1 + ω2 ) |c2 (t)|2
dt
= (PA ∝ v 4 ) + (PB ∝ v 2 )
Scheel & Buhmann (Phys Rev A 2009)
process ‘A’: resonance condition 0 = ω1 − k1 · v + ω2 − k2 · v = ω10 + ω20
process ‘B’: Ω = ω1 − k1 · v resonant decay
g Κ1 Κ2
eΚ
gΚ
One-photon + excitation power
g → e + hν
Z
d
P1 = dκ h̄(Ω+ω) |c1 (t)|2 ∝ −v 2
dt
total power P1 + P2 ∝ v 4
e vac
g vac
friction force F ∝ v 3
6= Barton 2010
Summary & Perspectives
Understanding heat transfer
• (meta)material properties: µ, ε(ω), σ(k, ω) . . .
• geometry: far/near field, shadows, diffraction . . .
• (local) temperature: e.m. sources, field correlations, local equilibrium (or not)
• un-known sources: fluctuating adsorbates
Safavi-Naini & al (Phys Rev A 2011)
un-known driven (non-eq) state: ground/excited atom, relevant time scales
Reducing heat transfer
• applications:
small, ultracold, trapped particles
← ‘IANV hybrids’
• reduce emission = reduce absorption
• (meta)material design: strips, conductivity, temperature
www.quantum.physik.uni-potsdam.de
New York Aug 2015