Bath-Assisted Cooling of Spins

Abstract

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...

Explanation of the Gibbs paradox within the framework of quantum thermodynamics

“…Such a possibility is offered by the field of quantum thermodynamics, that has been considered in recent years by several groups, see e.g. [18,19,22,27,30,31,32,34,36,40,41,42,43,44].…”

Thermodynamic limits of dynamic cooling

“…16 If the environmental coupling is not weak, the local energy has to be properly defined; see [29] for a concrete proposal (LEMBAS principle). 17 Conversely, if the unattainability of the absolute zero is regarded to be a law of nature, it can constrain the microscopic processes of environmental coupling and selective measurement. Albeit this possibility contradicts to the current paradigm of deriving the laws of thermodynamics from microscopic theories, it needs to be taken seriously.…”

“…When trying to do without a pre-existing cold bath different strategies are needed: Low temperatures can alternatively be produced dynamically from an initially equilibrium system via cyclic action of an external field [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. In this case the resulting cooled state should be exploited before the system has time to relax back to equilibrium.…”

Semioptimal practicable algorithmic cooling

“…Last but not least, in real life, the reset spins do not relax infinitely faster than the computation spins (see [36][37][38][39][40][41] for viewing AC as a novel type of heat-engine). Let R denote the ratio between the relaxation time of the computation spins and the relaxation time of the reset spins, R = T 1 (comp.…”