We experimentally explore the validity of the Jarzynski and W\'ojcik quantum heat-exchange fluctuation relation by implementing an interferometric technique in liquid-state nuclear magnetic resonance setup and study the heat-exchange statistics between two coupled spin-1/2 quantum systems. We experimentally emulate two models---(i) the XY-coupling model, containing an energy conserving interaction between the qubits, and (ii) the XX-coupling model---and analyze the regimes of validity and violation of the fluctuation symmetry when the composite system is prepared in an uncorrelated initial state with individual spins prepared in local Gibbs thermal states at different temperatures. We further extend our analysis for heat exchange by incorporating correlation in the initial state. We support our experimental findings by providing exact analytical results. Our experimental approach is general and can be systematically extended to study heat statistics for more complex out-of-equilibrium many-body quantum systems.We experimentally explore the validity of the Jarzynski and W\'ojcik quantum heat-exchange fluctuation relation by implementing an interferometric technique in liquid-state nuclear magnetic resonance setup and study the heat-exchange statistics between two coupled spin-1/2 quantum systems. We experimentally emulate two models---(i) the XY-coupling model, containing an energy conserving interaction between the qubits, and (ii) the XX-coupling model---and analyze the regimes of validity and violation of the fluctuation symmetry when the composite system is prepared in an uncorrelated initial state with individual spins prepared in local Gibbs thermal states at different temperatures. We further extend our analysis for heat exchange by incorporating correlation in the initial state. We support our experimental findings by providing exact analytical results. Our experimental approach is general and can be systematically extended to study heat statistics for more complex out-of-equilibrium many-body quantum systems.

arXiv:1811.07291Physical Review AOct 24, 201937 citations

Ruby NMR laser: A phenomenon of spontaneous self-organization of a nuclear spin system

Peter Boesiger, Ernst Brun, D. Meier

Radio wave amplification by stimulated emission of radiation (NMR laser) was observed in ${\mathrm{Al}}_{2}$ ${\mathrm{O}}_{3}$ : ${\mathrm{Cr}}^{3+}$ (ruby) with the $^{27}\mathrm{Al}$ spin system pumped to an inverted Zeeman state by means of dynamic nuclear polarization (DNP) and with an LC circuit tuned to the NMR transitions. A theory is developed which combines standard Bloch equations with the dynamic equations of a heat-reservoir model for the spin dynamics. Experimental data concerning the relaxation and polarization mechanisms in the nonradiant state are presented, and the parameters of the reservoir model are determined. In accord with these results, dynamic NMR laser equations for different modes of operation (continuous or pulsed) are derived from which the threshold of the NMR laser, its critical behavior near threshold, and its transient response after $Q$ -switch tuning can be calculated. The agreement between theory and experiments in the superradiant state reflects unambiguously the interplay between nuclear-spin relaxation, DNP, spin fluctuations, and the self-induced ordering of the $^{27}\mathrm{Al}$ spins perpendicular to the applied field. In particular, the results highlight the decisive role of the electronic dipole-dipole system in the spin and NMR laser dynamics of ruby. Special emphasis is placed on the close relationship between the NMR laser, as a system far from thermal equilibrium which shows the phenomenon of cooperative self-organization, and a system at thermal equilibrium which undergoes a second-order phase transition. Thus, the rotating nuclear-spin magnetization is treated as an order parameter.Radio wave amplification by stimulated emission of radiation (NMR laser) was observed in ${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$: ${\mathrm{Cr}}^{3+}$ (ruby) with the $^{27}\mathrm{Al}$ spin system pumped to an inverted Zeeman state by means of dynamic nuclear polarization (DNP) and with an LC circuit tuned to the NMR transitions. A theory is developed which combines standard Bloch equations with the dynamic equations of a heat-reservoir model for the spin dynamics. Experimental data concerning the relaxation and polarization mechanisms in the nonradiant state are presented, and the parameters of the reservoir model are determined. In accord with these results, dynamic NMR laser equations for different modes of operation (continuous or pulsed) are derived from which the threshold of the NMR laser, its critical behavior near threshold, and its transient response after $Q$-switch tuning can be calculated. The agreement between theory and experiments in the superradiant state reflects unambiguously the interplay between nuclear-spin relaxation, DNP, spin fluctuations, and the self-induced ordering of the $^{27}\mathrm{Al}$ spins perpendicular to the applied field. In particular, the results highlight the decisive role of the electronic dipole-dipole system in the spin and NMR laser dynamics of ruby. Special emphasis is placed on the close relationship between the NMR laser, as a system far from thermal equilibrium which shows the phenomenon of cooperative self-organization, and a system at thermal equilibrium which undergoes a second-order phase transition. Thus, the rotating nuclear-spin magnetization is treated as an order parameter.

Physical Review AAug 1, 197846 citations

From Large to Small Spin Systems: Exploring Many-body Effects in NMR

Yanqun Dong, Dale Li, Rona Ramos +1 more

Bulletin of the American Physical SocietyMar 15, 20060 citations

NMR Model for studying Decoherence

愛岩倉, Masamitsu Bando, Yasushi Kondo

理工学総合研究所研究報告Feb 1, 20150 citations

Collective behaviours in interacting spin systems

Inés Rodríguez-Arias

Dynamic nuclear polarization (DNP) is one of the most promising techniques towards a new generation of Magnetic Resonance Imaging (MRI). The idea is to use the Nuclear Magnetic Resonance (NMR) in other nuclei rather than the traditional hydrogen, such as carbon. For the carbon signal to be detected, one needs to enhance its spin polarization. In thermal equilibrium — at low temperature and high magnetic field — electron spins are far more polarized than any system of nuclear spins, which is due to their smaller mass. With the DNP technique we bring the system out-of-equilibrium irradiating it with microwaves. This triggers polarization transfer from the electron spins to the nuclear ones. During my Ph.D, I have studied both analytically and numerically the competition between the dipolar interactions among electron spins (which can be tuned experimentally) and the disorder naturally present in the sample. I proposed two models to study DNP: a Heisenberg spin-chain and a system free-fermions in the Anderson model. Two different regimes were found : For strongly interacting electron spins, the out-of-equilibrium steady state displays an effective thermodynamic behavior characterised by a very low spin temperature. In the weakly interacting regime, it is not possible to define a spin temperature, and it is associated to a many-body localized phase (or an Anderson-localized phase). My research was focused on the properties of the two phases with respect to the performance of DNP, and I found it to be optimal at the transition between the two. This is a very important result that has been verified by recent experiments carried in École Normale Supérieure de Paris.Dynamic nuclear polarization (DNP) is one of the most promising techniques towards a new generation of Magnetic Resonance Imaging (MRI). The idea is to use the Nuclear Magnetic Resonance (NMR) in other nuclei rather than the traditional hydrogen, such as carbon. For the carbon signal to be detected, one needs to enhance its spin polarization. In thermal equilibrium — at low temperature and high magnetic field — electron spins are far more polarized than any system of nuclear spins, which is due to their smaller mass. With the DNP technique we bring the system out-of-equilibrium irradiating it with microwaves. This triggers polarization transfer from the electron spins to the nuclear ones. During my Ph.D, I have studied both analytically and numerically the competition between the dipolar interactions among electron spins (which can be tuned experimentally) and the disorder naturally present in the sample. I proposed two models to study DNP: a Heisenberg spin-chain and a system free-fermions in the Anderson model. Two different regimes were found : For strongly interacting electron spins, the out-of-equilibrium steady state displays an effective thermodynamic behavior characterised by a very low spin temperature. In the weakly interacting regime, it is not possible to define a spin temperature, and it is associated to a many-body localized phase (or an Anderson-localized phase). My research was focused on the properties of the two phases with respect to the performance of DNP, and I found it to be optimal at the transition between the two. This is a very important result that has been verified by recent experiments carried in École Normale Supérieure de Paris.

Sep 27, 20180 citations

Radio wave amplification by stimulated emission of radiation (NMR laser) was observed in

{\mathrm{Al}}_{2}

{\mathrm{O}}_{3}

{\mathrm{Cr}}^{3+}

(ruby) with the

^{27}\mathrm{Al}

spin system pumped to an inverted Zeeman state by means of dynamic nuclear polarization (DNP) and with an LC circuit tuned to the NMR transitions. A theory is developed which combines standard Bloch equations with the dynamic equations of a heat-reservoir model for the spin dynamics. Experimental data concerning the relaxation and polarization mechanisms in the nonradiant state are presented, and the parameters of the reservoir model are determined. In accord with these results, dynamic NMR laser equations for different modes of operation (continuous or pulsed) are derived from which the threshold of the NMR laser, its critical behavior near threshold, and its transient response after

Q

-switch tuning can be calculated. The agreement between theory and experiments in the superradiant state reflects unambiguously the interplay between nuclear-spin relaxation, DNP, spin fluctuations, and the self-induced ordering of the

^{27}\mathrm{Al}

spins perpendicular to the applied field. In particular, the results highlight the decisive role of the electronic dipole-dipole system in the spin and NMR laser dynamics of ruby. Special emphasis is placed on the close relationship between the NMR laser, as a system far from thermal equilibrium which shows the phenomenon of cooperative self-organization, and a system at thermal equilibrium which undergoes a second-order phase transition. Thus, the rotating nuclear-spin magnetization is treated as an order parameter.