We show that work can be extracted from a two-level system (spin) coupled to a bosonic thermal bath. This is possible due to different initial temperatures of the spin and the bath, both positive (no spin population inversion) and is realized by means of a suitable sequence of sharp pulses applied to the spin. The extracted work can be of the order of the response energy of the bath, therefore much larger than the energy of the spin. Moreover, the efficiency of extraction can be very close to its maximum, given by the Carnot bound, at the same time the overall amount of the extracted work is maximal. Therefore, we get a finite power at efficiency close to the Carnot bound.The effect comes from the backreaction of the spin on the bath, and it survives for a strongly disordered (inhomogeneously broadened) ensemble of spins. It is connected with generation of coherences during the work-extraction process, and we derived it in an exactly solvable model. All the necessary general thermodynamical relations are derived from the first principles of quantum mechanics and connections are made with processes of lasing without inversion and with quantum heat engines.
A recently introduced class of quantum spherical spin models is considered in detail. Since the spherical constraint already contains a kinetic part, the Hamiltonian need not have kinetic term. As a consequence, situations with or without momenta in the Hamiltonian can be described, which may lead to different symmetry classes. Two models that show this difference are analyzed. Both models are exactly solvable and their phase diagram is analyzed. A transversal external field leads to a phase transition line that ends in a quantum critical point. The two considered symmetries of the Hamiltonian considered give different critical phenomena in the quantum critical region. The model with momenta is argued to be analog to the large-N limit of an SU(N ) Heisenberg ferromagnet, and the model without momenta shares the critical phenomena of an SU(N ) Heisenberg antiferromagnet.
A suitable sequence of sharp pulses applied to a spin coupled to a bosonic bath can cool its state, i.e., increase its polarization or ground state occupation probability. Starting from an unpolarized state of the spin in equilibrium with the bath, one can reach very low temperatures or sizeable polarizations within a time shorter than the decoherence time. Both the bath and external fields are necessary for the effect which comes from the backreaction of the spin on the bath. This method can be applied to cool at once a disordered ensemble of spins. Since the bath is crucial for this mechanism, the cooling limits are set by the strength of its interaction with the spin(s).PACS numbers: 05.30.-d,76.20.+q Cooling, i.e. obtaining relatively pure states from mixed ones, is of central importance in fields dealing with quantum features of matter. Laser cooling of motional states of atoms is nowadays a known achievement [1]. The related problem of cooling spins is equally known: it originated as an attempt to improve the sensitivity of NMR/ESR spectroscopy [2,3,4,5,6,7], since in experiments the signal strength is proportional to the polarization. Recently it got renewed attention due to realizations of setups for quantum computers [8]. The very problem arises since the most direct methods of cooling spins, such as lowering the temperature of the whole sample or applying strong dc fields, are not feasible or not desirable, e.g. in biological applications of NMR. Indeed, at temperature T = 1K and magnetic field B = 1T the equilibrium polarization of a proton is only tanh µB 2kBT = 10 −3 since the ratio µ = frequency field is equal to 42 MHz/T. For an electron µ is 10 3 times larger and for 15 N it is 10 times smaller. The weak polarization can be often compensated by a large number of spins, but for some NMR-isotopes the natural abundance is too low (0.36% for 15 N).Over the years, several methods were proposed to attack the problem of small polarizations. The polarization is generally increased via a dynamical process and it is used before relaxing back to equilibrium [2,3,4,5,6,7]. Specially known are methods where a relatively high polarization is transferred from one place to another, e.g. from electronic to nuclear spins [2,3,4,5,6]. In this respect electronic spins play the same role as the zerotemperature bath of vacuum modes employed for laser cooling of atoms [1] (this bath is typically inadequate for cooling nuclear spins, but can be employed to study cooling of atomic few-level systems in the context of optimal control theory [9]). Polarization transfer was studied in various settings both theoretically and experimentally [2,3,4,5,6]. However, this scheme is limited -besides requiring an already existing high polarization-by the availability and efficiency of the transfer interaction. A related method, polarization compression, consists in manipulating a set of n spins in such a way that the polarization of one spin is increased at the expense of decreasing the polarization of the remaining n − 1 spins. T...
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