1. Single reservoir heat engine: controlling the spin
Joan Vaccaro Centre for Quantum Dynamics Griffith University Brisbane, Australia
Steve Barnett
SUPA University of Strathclyde Glasgow, UK

2. Introduction Q 2nd law : Maxwell’s demon 1871 Kelvin-Planck 1851
It is impossible for a heat engine to produce net work in a cycle if it exchanges heat only with bodies at a single fixed temperature.
Maxwell’s demon 1871
demon extracts work of Q from thermal reservoir by collecting only hot gas particles.
hot
hot
Maxwell conceived a thought experiment as a way of furthering the understanding of the second law. His description of the experiment is as follows:[6]
... if we conceive of a being whose faculties are so sharpened that he can follow every molecule in its course, such a being, whose attributes are as essentially finite as our own, would be able to do what is impossible to us. For we have seen that molecules in a vessel full of air at uniform temperature are moving with velocities by no means uniform, though the mean velocity of any great number of them, arbitrarily selected, is almost exactly uniform. Now let us suppose that such a vessel is divided into two portions, A and B, by a division in which there is a small hole, and that a being, who can see the individual molecules, opens and closes this hole, so as to allow only the swifter molecules to pass from A to B, and only the slower molecules to pass from B to A. He will thus, without expenditure of work, raise the temperature of B and lower that of A, in contradiction to the second law of thermodynamics....
heat engine Q

3. ? ? Landauer erasure Erasure is irreversible
Landauer, IBM J. Res. Develop. 5, 183 (1961)
Erasure is irreversible
forward process:
time reversed: ? ? 1 1
Hide the past of the memory in a reservoir (whose past is unknown)
Minimum cost
BEFORE erasure
environment
AFTER erasure
0/1
entropy
# microstates

4. Impact Q Q Q cycle No net gain entropy erased memory work
1982 Bennet showed a full cycle requires the erasure of demon’s memory which costs at least Q : Q
hot
Bennett, Int. J. Theor. Phys. 21, 905 (1982) Q
erased memory
work
Q
heat engine
cycle
entropy
hot
No net gain

5. Different Paradigm Conventional Paradigm
 maximisation of entropy subject to
conservation of energy
 cost of erasure is work
Different Paradigm
 all states are degenerate in energy
 maximisation of entropy subject to
conservation of angular momentum
 cost of erasure is loss of angular momentum

6. Erasure using spin reservoir
Reservoir as “canonical” ensemble (exchanging not energy)
Reservoir:
Maximise entropy
subject to
eigenvalue degeneracy

7. Erasure using spin reservoir
Reservoir as “canonical” ensemble (exchanging not energy)
Reservoir:
Maximise entropy
subject to
spin disorder
eigenvalue degeneracy

8. Hide the state of the memory in a SPIN reservoir
1st Law:
Minimum cost
BEFORE erasure
spin reservoir
AFTER erasure
entropy =
entropy =
0/1
entropy =

9. That’s the principle,
but can the erasure be done in practice?

10. Energy-degenerate spin reservoirs
Optical dipole trap (far off-resonant laser fields create spatially-dependent light shifts)
trap frequencies Hz
temperatures ~K
lifetimes ~40 s
numbers
focused laser
optical dipole trap
trapped gas
vibrational frequency
Ketterle, Pritchard et al., Phys. Rev. Lett. 90, (2003)

11. Erasure using a spin reservoir
 single-electron atoms with ground state spin angular momentum
 memory: spin-1 atoms in equal mixture
 reservoir: spin-1/2 atoms all in mj = -1/2 state (spin polarised)
 independent optical trapping potentials (dipole traps)
 atoms exchange spin angular momentum via collisions when traps brought together
 erasure of memory by loss of spin polarisation of reservoir – the cost of erasure is spin angular momentum
-1/2
1/2
-1/2
1/2
-1/2
1/2
reservoir 1 2 3 -1 1
memory

12. Erasure using a spin reservoir
 single-electron atoms with ground state spin angular momentum
 memory: spin-1 atoms in equal mixture
 reservoir: spin-1/2 atoms all in mj = -1/2 state (spin polarised)
 independent optical trapping potentials (dipole traps)
 atoms exchange spin angular momentum via collisions when traps brought together
 erasure of memory by loss of spin polarisation of reservoir – the cost of erasure is spin angular momentum
-1/2
1/2
-1/2
1/2
-1/2
1/2
reservoir 1 2 3 -1 1
memory

13. Q Q Lets put this erasure process to work in a heat engine… cycle
hot
hot
entropy
work
Q
erased memory
work
No net gain Q
heat engine 13

14. T1 Q …like this… cycle Gain if T1 > 0 spin reservoir
increased entropy
spin
cycle
entropy
hot
hot T1
work
Gain if T1 > 0 Q
heat engine

15. Optical work and heat engines
Scovil (1959):
Phys. Rev. Lett. 2, (1959)
J. Chem. Phys. 67, 5676 (1977)
“...the complete conversion, possible in principle, of coherent radiation into work...”

16. Heat engine using a spin reservoir
working fluid
hyperfine electronic states
optical dipole trap
vibrational energy states
of trapping potential
vibrational frequency
trapped atomic gas

17. Extracting heat as coherent light
working fluid
Raman p pulse
temperature T
atoms
atoms
photons absorbed
net gain in energy of
coherent light
photons emitted

18. Erasing the memory using spin reservoir
working fluid
hot
memory
optical dipole trap

19. Erasing the memory using spin reservoir
working fluid
spin reservoir
spin disorder
hot
memory
temperature T
exchange spin & energy
optical dipole traps
overlap gases
& then separate

20. Erasing the memory using spin reservoir
working fluid
spin reservoir
spin disorder
memory
temperature T
temperature T
Entropy is maximum for

21. spatial degree of freedom
Carnot heat engine
working fluid Q1 Q2
W = Q1 - Q2 T1 T2 S
cyclical
operation
spin disorder
New heat engine Q JZ
W = Q T
spatial degree of freedom
spin degree of freedom S E
working fluid
cyclical
operation JZ
. . . repeat cycle many times . . . 21

22. Optical work is extracted until…
Raman p pulse
spin disorder
same probability
same probability
# of “cycles”:
Total work extracted
for

23. spatial degree of freedom
Operation of heat engine – finite reservoirs
Carnot heat engine
working fluid Q1 Q2
W = Q1 - Q2 T1 T2 S
cyclical
operation
spin disorder
New heat engine Q JZ
W = Q T
spatial degree of freedom
spin degree of freedom S E
working fluid
cyclical
operation JZ

24. spatial degree of freedom
Summary
2nd Law is equivalent to Erasure of Information
cost of erasure depends on the conservation law
for a spin reservoir the cost is
where
new kind of heat engine Q JZ T
spatial degree of freedom
spin degree of freedom S W