Thermal and Dissipative effects in Casimir Physics

Thermal and Dissipative effects
in Casimir Physics
Roberto Onofrio
Department of Physics and Astronomy, Dartmouth College
Department of Physics “G. Galilei”, University of Padova
Motivations
Casimir force in a cylindrical-plane geometry
Electrostatic calibrations and parallelism
Detection of the dynamical Casimir effect
Conclusions
Les Houches, 6/6/2005

Motivations
– Casimir physics is a macroscopic manifestation of
quantum vacuum
• Many macroscopic manifestations of quantum mechanics
(black-body, body, specific heats, superfluidity and
superconductivity), very few of quantum vacuum
• Open window on renormalization issues in QED
– Casimir forces are a background to other
(hypothetical) forces in the micrometer range
– We need to understand the role of quantum
fluctuations in the acceleration of the universe
2

Parallel plates
Experimental configurations
Plane-sphere
Original configuration
proposed by Casimir,
“textbook” geometry,
clean theoretical
predictions based on
sum of modes
No sum of modes
approach, theoretical
interpretation relies on the
proximity force
approximation, under
control at the

Tests of Casimir force after the last decade are solid, but…
• For constraining extra-dimensional forces, we need to
master all the corrections to the “plain” Casimir force
• To understand the interplay between quantum
fluctuations and boundary conditions, we need
to study other geometries
In between a plane-plane and a plane-sphere there is
a plane-cylinder geometry
4

Predictably, the plane-cylinder configuration
has intermediate advantages and drawbacks
• With respect to the parallel plane configuration, it has
less parallelism and dust issues, but less signal
• With respect to the plane-sphere configuration, it has an
1D issue of parallelism, but more signal, and shares the
proximity force approximation issue
The starting point for the analysis is a configuration
with eccentric cylinders [Dalvit[
et al., EPL 67, 51 (2004) ]
5

Plane-cylindrical configuration: predictions
If we introduce the equivalent Casimir
force F 0 as twice the Casimir force
between parallel plates with the same
surface area as the cylinders we get,
in the two opposite limits, and using
the proximity force approximation:
F
≈
ε
b −
a
F
y 0
Small eccentricity
F
≈
5
32
2
⎛ b−a
⎜
⎝
d
⎞
⎟
⎠
7/ 2
F
y 0
Large eccentricity
6

→ ∞
In the limit of one gets the expression for
the Casimir force in a cylindrical-plane configuration
1/2
π 3 hc
La
F ≈
cp
384 2 7/ 2
The Casimir force scales as
, which is
intermediate between the slower scaling
d −3
−4
the plane-sphere and
of the plane-plane
d
d
d
−3.5
of
It looks more promising with respect to the other
geometries to study the thermal contribution to
the Casimir force
7

The combined conductivity-temperature corrections are larger
than in the parallel-plane situation for at least two different
models, the plasma model (a) and a model without the TE0
mode (b). Moreover, the predictions of the two models differ
by a factor of almost 2 around 3-4 micrometers for all
geometries.
Feasibility study for a measurement of the Casimir force in
the cylindrical-plane configuration around 4 micrometers
8

The prototype
Vacuum chamber
System of micropositioners
Pumping system
Optical digital microscope
Diode laser at 671 nm
Telescope and fiber launcher
Directional coupler
Fiber fed through chamber
9

Vacuum chamber close up
• Top micrometer (coarse) and PZT (fine) for optical fiber-resonator distance
• Bottom micrometer (coarse) and 2 x PZTs (fine) for distance control
(common mode) and for 1D parallelization (differential mode)
• Stainless steel,
5mm diameter
cylinder
• Stainless steel,
1cm x 2 cm x
0.11 mm resonator
(247 Hz)
• Lateral rotary
micrometer +
goniometer for
coarse parallelization
10

Electrostatic calibrations
The exact expression for the electrostatic force can be reduced, in the PFA limit, to:
1/2
F La
El
≅ π ε 0 2
3/ 2 V
4 2 d
The corresponding frequency-shift for an harmonic oscillator is:
∆ν
1/ 2
La V
2
2 3ε
0
= −
El 5/ 2
64π
2 mν
0 0
d
Signal from the photodiode
sent to a FFT analyzer
11

Parallelism procedure
Deviations from parallelism can be detected by studying
the dependence of the forces upon the “degree of parallelism”
F
F
np
np
5
≅ F 1+
α 2+
O(
α 4)
8
⎡
p ⎢
⎣
21
≅ F 1+
α 2 + O(
α 4)
8
⎡
p ⎢
⎣
⎤
⎥
⎦
⎤
⎥
⎦
Electrostatic
Casimir
Minimization of the force for a constant distance allows to find
the parallel configuration (very hard in the parallel case as a
2D optimization is necessary)
12

• Voltage on the 2 PZTs supplied
in differential mode, to leave
the central distance constant
(Vleft+Vright=const)
• Plot of squared frequency shift
versus bias voltage (above)
• Plot of the curvature of the
parabola versus the asymmetry
Vleft-Vright, and search for the
minimum
• Thermal drifts in resonator
frequency are important,
considering the duration of
the procedure
13

Currently we are taking data after installing a Peltier cooler
on the resonator support
Expected frequency shift due to the Casimir force:
∆ν
2
= −
7π
hc
mν
La
d 0
1/ 2
Cas 9/ 2
3072 2
0
To give a feeling, this is equivalent to the detection of a bias voltage:
V eq
=
⎛
⎜
⎝
πhc
96ε
0
⎞
⎟
⎠
1/2
1
d
=
11.05mV
d
A 1% accuracy measurement at 4 micrometers requires control of the
electrostatics at the level of about 0.03 mV
14

Dynamical Casimir effect
Very difficult task
– Lozovik et al., Yablonovitch,
Braggio et al., see talk by G. Ruoso
on INFN MIR proposal)
– Proposal using Rydberg atoms in
cavities (Dodonov(
et al., Lambrecht
et al)
– Use of nanoresonators and
hyperfine states (R.O., 2003):
6Li has a small hyperfine splitting
in the ground state, in a frequency
range where nanoresonators are
already available
15

Lithium Doppler-free spectroscopy
•Lithium vapor cells require temperatures
of the vapor of order 400 C
•Buffer gas (Ar) for mitigating diffusion on
the end windows
• Pump and probe beams scanned around
the D2 line of the transition
• Lockable signal for stabilizing diode lasers
16

Doppler-free absorption signal with the hyperfine
spectrum of the 2S1/2 (F=1/2) -> 2P3/2 and
2S1/2 (F=3/2) -> 2P3/2 (and their crossover)
Absorption signal + laser scanning
Absorption signal + Fabry-Perot signal
17

Differential absorption scheme
In assembly stage, a Lithium atomic
beam, two resonant laser beams +
a region for the “Casimir photons”
One possibility is to apply optical
pumping schemes to send all atoms
into the 2S1/2 (F=3/2) level and
to look to the presence in the other
hyperfine level after traveling
through the “Casimir region”
Development of nanoresonator
arrays as mechanical antennae
Development of a suitable
electromagnetic cavity to enhance
the signal
18

What is on the horizon…
Thermal contribution to the Casimir force
• Temperature stabilization of the setup
• Calibrations at smaller distances
• Novel micromechanical resonators (micromechanical
lab at the Thayer Engineering School at Dartmouth)
Dissipative contribution to the Casimir force
• Pumping scheme for Lithium
• Differential absorption with rf source
• Nanomechanical resonator arrays
Micro and nanomechanics + Atomic Physics
19

The people
Thermal effect
Dissipative effect
Scott Middleman (UG)
Jonathan Huang (UG)
Michael Brown-Hayes (G)
Nathan Monnig (UG)
Woo-Joong
Kim (G)
James Hayden-Brownell (RS)
Theory
Diego Dalvit (Los Alamos)
Fernando Lombardo (Buenos Aires)
Francisco Mazzitelli (Buenos Aires)
20