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

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

? ? 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

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

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

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

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

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 =

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

Energy-degenerate spin reservoirs Optical dipole trap (far off-resonant laser fields create spatially-dependent light shifts) trap frequencies 1-1000 Hz temperatures ~K lifetimes ~40 s numbers 1-106 focused laser optical dipole trap trapped gas vibrational frequency Ketterle, Pritchard et al., Phys. Rev. Lett. 90, 100404 (2003)

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

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

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

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

Optical work and heat engines Scovil (1959): Phys. Rev. Lett. 2, 262-263 (1959) J. Chem. Phys. 67, 5676 (1977) “...the complete conversion, possible in principle, of coherent radiation into work...”

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

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

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

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

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

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

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

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

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