Radiative cooling of a spin ensemble

Abstract

Physical systems reach thermal equilibrium through energy exchange with their environment, and for spins in solids the relevant environment is almost always the host lattice in which they sit. However, recent studies motivated by observations from Purcell showed how coupling to a cavity can become the dominant form of relaxation for spins, given suitably strong spin-cavity coupling. In this regime, the cavity electromagnetic field takes over from the lattice as the dominant environment, inviting the prospect of controlling the spin temperature independently from that of the lattice, by engineering a suitable cavity field. Here, we report on precisely such control over spin temperature, illustrating a novel and universal method of electron spin hyperpolarisation. By switching the cavity input between loads at different temperatures we can control the electron spin polarisation, cooling it below the lattice temperature. Our demonstration uses donor spins in silicon coupled to a superconducting micro-resonator and we observe an increase of spin polarisation of over a factor of two. This approach provides general route to signal enhancement in electron spin resonance, or indeed nuclear magnetic resonance through dynamical nuclear spin polarisation (DNP). When a physical system is coupled to several reservoirs at different temperatures, it equilibrates at an intermediate temperature which depends on the strength with which it is coupled to each bath. An electron spin in a solid is coupled to two different reservoirs: phonons in its host lattice, and microwave photons in its electromagnetic environment. The strength of this coupling is characterized by the rate at which the spin, of Larmor frequency ω spin , relaxes by spontaneously emitting a quantum of energy ω spin into each bath. In usual magnetic resonance experiments [5], the spin-lattice relaxation rate Γ phon is many orders of magnitude larger than the radiative relaxation rate Γ phot , so that the spin temperature T spin is determined by the sample temperature T phon regardless of the temperature of the microwave photons T phot .The strength of radiative relaxation can however be enhanced by coupling the spins resonantly to one mode of a microwave resonator of frequency ω 0 = ω spin , as discovered by Purcell [2,6,7]. The coupling strength is then given by Γ phot = 4g 2 /κ, g being the spin-photon coupling constant and κ the resonator mode relaxation rate. Superconducting micro-resonators can be designed with a small mode volume, which increases g, while retaining a high quality factor, which reduces κ. This makes it possible to reach the Purcell regime defined by Γ phot Γ phon , as demonstrated in recent experiments [1]. In this regime, T spin should thus be equal to T phot and no longer to T phon , and electron spin hyperpolarisation should be possible by cooling the microwave field down to a temperature T phot T phon . The simplest way to do so is to connect the resonator input to a cold 50 Ω resistor, as shown in Fig. 1a. As long as the coupling rate of th...

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