Download Quantized conductance for neutral matter

Quantized conductance for neutral matter
J.P. Brantut, S. Krinner, D. Stadler, D. Husmann, M. Lebrat and T. Esslinger
Institute for Quantum Electronics
ETH Zürich
Sunday, June 29, 14
Mesoscopic Devices
which size are comparable to the de Broglie wavelength of particles
Cold atoms and beyond
Sunday, June 29, 14
J-P Brantut
Mesoscopic Devices
which size are comparable to the de Broglie wavelength of particles
B. J. van Wees, H. van Houten, C. W. J. Beenakker, J. G. Williamson, L. P. Kouwenhoven, D. van der Marel, C. T. Foxon, Phys. Rev. LeD. 60, 848 (1988)
Cold atoms and beyond
Sunday, June 29, 14
D A Wharam, T J Thornton, R Newbury, M Pepper, H Ahmed, J E F Frost, D G Hasko, D C Peacock, D A Ritchie and G A C Jones, J. Phys. C: Solid State Phys. 21 L209 J-P Brantut
Conductance Quantization : Landauer theory
Left reservoir
Cold atoms and beyond
Sunday, June 29, 14
Right reservoir
J-P Brantut
Conductance Quantization : Landauer theory
Left reservoir
Right reservoir
Cold atoms and beyond
Sunday, June 29, 14
J-P Brantut
Conductance Quantization : Landauer theory
Left reservoir
Right reservoir
Group velocity
Density of states
Cold atoms and beyond
Sunday, June 29, 14
p
vg (✏) = 2✏/m
1
g1D (✏) =
2⇡~vg (✏)
J-P Brantut
Conductance Quantization : Landauer theory
Left reservoir
Right reservoir
p
vg (✏) = 2✏/m
1
g1D (✏) =
2⇡~vg (✏)
Group velocity
Density of states
Current
Cold atoms and beyond
Sunday, June 29, 14
I=
Z
EF + µ
EF
µ
g1D (✏)vg (✏)d✏ =
h
J-P Brantut
Universal conductance quantum 1/h
E
E
n
n
Left Reservoir
Cold atoms and beyond
Sunday, June 29, 14
Right Reservoir
J-P Brantut
Universal conductance quantum 1/h
Net current carriers
E
E
n
n
Left Reservoir
Cold atoms and beyond
Sunday, June 29, 14
Right Reservoir
J-P Brantut
Universal conductance quantum 1/h
µ
time
Heisenberg relation
Cold atoms and beyond
Sunday, June 29, 14
h
µ
J-P Brantut
Universal conductance quantum 1/h
µ
time
Heisenberg relation
h
µ
1 1 1 1
time
Pauli principle
Cold atoms and beyond
Sunday, June 29, 14
J-P Brantut
Universal conductance quantum 1/h
µ
time
Heisenberg relation
h
µ
1 1 1 1
time
Pauli principle
Cold atoms and beyond
Sunday, June 29, 14
µ
I=
h
J-P Brantut
Universal conductance quantum 1/h
No reference whatsoever to electric charges, fields etc
Cold atoms and beyond
Sunday, June 29, 14
J-P Brantut
Universal conductance quantum 1/h
No reference whatsoever to electric charges, fields etc
VOLUME 83, NUMBER 19
Journal of Low Temperature Physics, Vol. 141, Nos. 3/4, November 2005 (© 2005)
DOI: 10.1007/s10909-005-8223-3
PHYSICAL REVIEW LETTERS
8 NOVEMBER 1999
Quantum Point Contacts for Neutral Atoms
J. H. Thywissen,* R. M. Westervelt,† and M. Prentiss
On the Feasibility of Detecting Quantized Conductance
in Neutral Matter
Yuki Sato, Byeong-Ho Eom, and Richard Packard
Department of Physics, University of California, Berkeley, CA 94720-7300, USA
E-mail: [email protected]
(Received May 18, 2005; revised July 18, 2005)
Department of Physics, Harvard University, Cambridge, Massachusetts 02138
(Received 19 July 1999)
We show that the conductance of atoms through a tightly confining waveguide constriction is
quantized in units of l2dB !p, where ldB is the de Broglie wavelength of the incident atoms. Such a
constriction forms the atom analog of an electron quantum point contact and is an example of quantum
transport of neutral atoms in an aperiodic system. We present a practical constriction geometry that can
be realized using a microfabricated magnetic waveguide, and discuss how a pair of such constrictions
can be used to study the quantum statistics of weakly interacting gases in small traps.
PACS numbers: 03.75. – b, 05.60.Gg, 32.80.Pj, 73.40.Cg
LOW TEMPERATURE PHYSICS
VOLUME 34, NUMBERS 4–5
APRIL-MAY 2008
to-width ratio of "105 . This new regime is interesting
Quantum transport, in which the center-of-mass motion
of particles is dominated by quantum mechanical effects,
because deleterious effects such as reflection and interHELIUM
When an electrochemical potential difference (i.e., a voltage) is appliedLIQUID
has been
observed in both electron and neutral-atom
mode nonadiabatic transitions are minimized [12], allowacross a metal wire whose transverse dimensions are on the order of the systems. Pioneering experiments demonstrated quantum
ing for accuracy of conductance quantization limited only
3
electron’s Fermi wavelength, the conductance G ≡ I /!V becomes quantizedQuantum-limited
transport in periodic
structures.
example,
mass
flow ofFor
liquid
HeBloch by finite-temperature effects. Furthermore, the observa2
in units of 2e / h. We present calculations that show that when a chemical oscillations and Wannier-Stark ladders were observed in
tion of conductance quantization at new energy and length
G. Lambertofand
G. Gervais
potential difference !µ3 is applied across an array of small apertures whose the conduction
electrons
through superlattices [1] with
scales is of inherent interest.
sizes are comparable to the !Fermi wavelength
of 3He in a 3He:4 He mixture, an applied
electric
field,McGill
as well
as in the
transport
of
If a QPC
for neutral atoms were realized, it would
"
Department
of Physics,
University,
3600
rue Université,
Montréal,
Qc, Canada
2
accelerating optical lattices [2,3].
provide excellent opportunities for exploring the physics
the mass conductance G ≡ !µI3/m∗ will be quantized in units of 2m∗3 / h neutral atoms through
a!
3
W. J.work
Mullin
3
Further
with neutral atoms in optical lattices has
of small ensembles of weakly interacting gases. For
where m∗3 is the 3He effective mass. We show that the mass conductance will utilized their slower time scales (kHz instead of THz) and
instance, the01003,
transmission
through a series of two QPC’s
Department
of Physics, University of Massachusetts, Amherst, Massachusetts
USA
be quantized for a 0.1% mixture passing through 10 nm diameter pores at longer coherence
lengths29,to2007"
observe a clear signature of
would depend on the energetics of atoms confined in the
!Submitted October
temperatures below 25 mK. The phenomenon should be observable in a filter dynamical Bloch band suppression [4], an effect originally
trap between the two constrictions. The physics of such a
Fiz. Nizk. Temp. 34, 321–325 !April–May 2008"
material made by nuclear track etching.
predicted for but not yet observed in electron transport [5].
“quantum dot” for atoms is fundamentally different from
Quantum
transport
also occurs
in aperiodic
systems.unusual
that quantum
of electrons,
since theinCoulombic
charging energy
We consider
theoretically
the possibility
of observing
fluid behavior
liquid
3
3
4
KEY WORDS: conductance; Fermi wavelength; quasiparticle; ballistic For example,
a quantum
(QPC)confined
is a single
that dominates
the energetics
of an electron quantum
He and solutions
of point
He in contact
He systems
to nanochannels.
In the case
of pure ballistic
transport.
constriction
through
the conductance
is always
anquantized
dot [13]
is absent
The quantum
/ h. neutral
We showparticles.
that
flow at very
low which
temperature
the conductance
will be
in units
of 2m2for
Cold atoms and beyond
J-P Brantut
integer
of some
base conductance.
quanstatistics
atoms
energetically
thesemultiple
steps should
be sensitive
to increases The
in temperature.
We also of
useneutral
a random
scattering
ma- restricted to sub2
tization
of electrontoconductance
in multiples
of 2escattering.
three-dimensional
spacesfluctuations
has already aroused theoretical
!h,
trix simulation
study flow with
diffusive wall
Universal conductance
Sunday, June 29, 141. INTRODUCTION
in novel
effects
such as the
fermionization [14] and
where
e
is
the
charge
of
the
electron
and
h
is
Planck’s
analogous to those seen in electron systems should then beinterest
observable.
Finally
we consider
Experimental setup
7.5 104 6Li atoms
T ~ 0.11 TF
TF = 352 nK
Cold atoms and beyond
Sunday, June 29, 14
J-P Brantut
Experimental setup : cloud shaping
Cold atoms and beyond
Sunday, June 29, 14
J-P Brantut
Experimental setup : cloud shaping
Cold atoms and beyond
Sunday, June 29, 14
J-P Brantut
Experimental setup : cloud shaping
Binary mask
Gaussian beam (@ 532 nm)
Microscope objective
Demagnification x11
Images a “split gate” onto the atoms
Cold atoms and beyond
Sunday, June 29, 14
J-P Brantut
Experimental setup : cloud shaping
Attractive “Gate” potential
Gaussian envelope (@ 767 nm)
Cold atoms and beyond
Sunday, June 29, 14
J-P Brantut
Experimental setup : cloud shaping
c
d
Z
E2
µ
E1
Cold atoms and beyond
Sunday, June 29, 14
E0
1
J-P Brantut
0
Energy / kB (µK)
10 µm
Experimental setup : cloud shaping
c
b
Mask
Lens
e
10 µm
E(ky)
e
d
Z
E2
x-frequency
Cloud
0
Cold atoms and beyond
Sunday, June 29, 14
ky
-40
-20
30 µkHz
E1
z-frequency
0
10 kHz
E0
0
1
Energy / kB (µK)
Dichroic
mirror
20
40
Channel ground
state
Position
y (µm)
1 µK
Chemical potential
0.32 µK
Temperature
42 nK
Gate Potential
0 - 3 µK
J-P Brantut
Experimental setup : cloud shaping
c
b
Mask
Lens
e
10 µm
E(ky)
e
d
Z
E2
x-frequency
Cloud
0
Cold atoms and beyond
Sunday, June 29, 14
ky
-40
-20
30 µkHz
E1
z-frequency
0
10 kHz
E0
0
Contact ground
state
Position
y (µm)
1
Energy / kB (µK)
Dichroic
mirror
20
40
1 µK
Chemical potential
0.352 µK
Temperature
42 nK
Gate Potential
0 - 3 µK
J-P Brantut
Measurement
E(k)"
!"!
!#!
k"
Cold atoms and beyond
Sunday, June 29, 14
J-P Brantut
Measurement
E(k)"
!"!
!#!
k"
Cold atoms and beyond
Sunday, June 29, 14
J-P Brantut
Measurement
E(k)"
!"!
!#!
k"
Cold atoms and beyond
Sunday, June 29, 14
J-P Brantut
Measurement
E(k)"
!"!
!#!
k"
Landauer theory
No free parameter
Cold atoms and beyond
Sunday, June 29, 14
J-P Brantut
Measurement
E(k)"
!"!
!#!
k"
⌫z = 10.4 kHz
⌫z = 8.2 kHz
Cold atoms and beyond
Sunday, June 29, 14
J-P Brantut
Measurement
⌫z = 10.4 kHz
⌫z = 8.2 kHz
Cold atoms and beyond
Sunday, June 29, 14
J-P Brantut
Varying the split gate strength
Cold atoms and beyond
Sunday, June 29, 14
J-P Brantut
What do we learn ?
Cold atoms and beyond
Sunday, June 29, 14
J-P Brantut
It works...
... with neutral particles: no forces are applied to the atoms
Cold atoms and beyond
Sunday, June 29, 14
J-P Brantut
It works...
... with neutral particles: no forces are applied to the atoms
... with closed, microcanonical reservoirs: only elastic processes
take place in the reservoirs, no dissipative dynamics
Cold atoms and beyond
Sunday, June 29, 14
J-P Brantut
It works...
... with neutral particles: no forces are applied to the atoms
... with closed, microcanonical reservoirs: only elastic processes
take place in the reservoirs, no dissipative dynamics
... with very little interparticle scattering in the reservoirs: mean
free path much larger than the cloud size
Wide control over the reservoirs dynamics
Cold atoms and beyond
Sunday, June 29, 14
J-P Brantut
Wide tunability of the geometry
Using “optical lithography”, any geometry can be implemented
Cold atoms and beyond
Sunday, June 29, 14
J-P Brantut
Wide tunability of the geometry
Using “optical lithography”, any geometry can be implemented
Example: quantum wire with sharper edges
In-situ picture of the potential
shape
Cold atoms and beyond
Sunday, June 29, 14
J-P Brantut
Wide tunability of the geometry
Using “optical lithography”, any geometry can be implemented
Example: quantum wire with sharper edges
In-situ picture of the
potential shape
Cold atoms and beyond
Sunday, June 29, 14
J-P Brantut
Conclusions and perspectives
Strongly interacting gases: BEC-BCS crossover
Cold atoms and beyond
Sunday, June 29, 14
J-P Brantut
Conclusions and perspectives
Strongly interacting gases: BEC-BCS crossover
Engineering reservoirs: non thermal, coherent, small size
Cold atoms and beyond
Sunday, June 29, 14
J-P Brantut
Conclusions and perspectives
Strongly interacting gases: BEC-BCS crossover
Engineering reservoirs: non thermal, coherent, small size
Other transport coefficients: heat conductance, thermopower
J.P. Brantut et al, Science 342, 713 (2013)
Cold atoms and beyond
Sunday, June 29, 14
J-P Brantut
Charles Grenier
JPB
Sebastian Krinner
Dominik Husmann
Martin Lebrat
Tilman Esslinger
arXiv:1404.6400
Discussions: C. Chin, W. Zwerger, T. Ihn, K. Ensslin, Y. Imry, G. Blatter, A. Georges, T. Giamarchi
Cold atoms and beyond
Sunday, June 29, 14
J-P Brantut