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Register a new userDynamics of the collective modes of an inhomogeneous spin ensemble in a cavity
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We study the excitation dynamics of an inhomogeneously broadened spin ensemble coupled to a single cavity mode. The collective excitations of the spin ensemble can be described in terms of generalized spin waves and, in the absence of the cavity, the free evolution of the spin ensemble can be described as a drift in the wave number without dispersion. In this article we show that the dynamics in the presence of coupling to the cavity mode can be described solely by a modified time evolution of the wave numbers. In particular, we show that collective excitations with a well- defined wave number pass without dispersion from negative to positive valued wave numbers without populating the zero wave number spin wave mode. The results are relevant for multi-mode collective quantum memories where qubits are encoded in different spin waves.
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We study experimentally and theoretically a dense ensemble of negatively charged nitrogen-vacancy centers in diamond coupled to a high $Q$ superconducting coplanar waveguide cavity mode at low temperature. The nitrogen-vacancy centers are modeled as effective spin one defects with inhomogeneous frequency distribution. For a large enough ensemble the effective magnetic coupling of the collective spin dominates the mode losses and inhomogeneous broadening of the ensemble and the system exhibits well resolved normal mode splitting in probe transmission spectra. We use several theoretical approaches to model the probe spectra and the number and frequency distribution of the spins. This analysis reveals an only slowly temperature dependent q-Gaussian energy distribution of the defects with a yet unexplained decrease of effectively coupled spins at very low temperatures below $unit{100}{millikelvin}$. Based on the system parameters we predict the possibility to implement an extremely stable maser by adding an external pump to the system.
We achieve the strong coupling regime between an ensemble of phosphorus donor spins in a highly enriched $^{28}$Si crystal and a 3D dielectric resonator. Spins were polarized beyond Boltzmann equilibrium using spin selective optical excitation of the no-phonon bound exciton transition resulting in $N$ = $3.6cdot10^{13}$ unpaired spins in the ensemble. We observed a normal mode splitting of the spin ensemble-cavity polariton resonances of 2$gsqrt{N}$ = 580 kHz (where each spin is coupled with strength $g$) in a cavity with a quality factor of 75,000 ($gamma ll kappa approx$ 60 kHz where $gamma$ and $kappa$ are the spin dephasing and cavity loss rates, respectively). The spin ensemble has a long dephasing time (T$_2^*$ = 9 $mu$s) providing a wide window for viewing the dynamics of the coupled spin ensemble-cavity system. The free induction decay shows up to a dozen collapses and revivals revealing a coherent exchange of excitations between the superradiant state of the spin ensemble and the cavity at the rate $gsqrt{N}$. The ensemble is found to evolve as a single large pseudospin according to the Tavis-Cummings model due to minimal inhomogeneous broadening and uniform spin-cavity coupling. We demonstrate independent control of the total spin and the initial Z-projection of the psuedospin using optical excitation and microwave manipulation respectively. We vary the microwave excitation power to rotate the pseudospin on the Bloch sphere and observe a long delay in the onset of the superradiant emission as the pseudospin approaches full inversion. This delay is accompanied by an abrupt $pi$ phase shift in the peusdospin microwave emission. The scaling of this delay with the initial angle and the sudden phase shift are explained by the Tavis-Cummings model.
We consider dynamics of a disordered ensemble of qubits interacting with single mode photon field, which is described by exactly solvable inhomogeneous Dicke model. In particular, we concentrate on the crossover from few-qubit systems to the system of many qubits and analyze how collective behavior of coupled qubits-cavity system emerges despite of the broadening. We show that quantum interference effects survive in the mesoscopic regime -- dynamics of an entangled Bell state encoded into the qubit subsystem remains highly sensitive to the symmetry of the total wave function. Moreover, relaxation of these states is slowed down due to the formation of collective dark states weakly coupled to light. Dark states also significantly influence dynamics of excitations of photon subsystem by absorbing them into the qubit subsystem and releasing quasiperiodically in time. We argue that predicted phenomena can be useful in quantum technologies based on superconducting qubits. For instance, they provide tools to deeply probe both collective and quantum properties of such artificial macroscopic systems.
When the dynamics of a spin ensemble are expressible solely in terms of symmetric processes and collective spin operators, the symmetric collective states of the ensemble are preserved. These many-body states, which are invariant under particle relabeling, can be efficiently simulated since they span a subspace whose dimension is linear in the number of spins. However, many open system dynamics break this symmetry, most notably when ensemble members undergo identical, but local, decoherence. In this paper, we extend the definition of symmetric collective states of an ensemble of spin-1/2 particles in order to efficiently describe these more general collective processes. The corresponding collective states span a subspace which grows quadratically with the number of spins. We also derive explicit formulae for expressing arbitrary identical, local decoherence in terms of these states.
We study the dynamics of a spin ensemble strongly coupled to a single-mode resonator driven by external pulses. When the mean frequency of the spin ensemble is in resonance with the cavity mode, damped Rabi oscillations are found between the spin ensemble and the cavity mode which we describe very accurately, including the dephasing effect of the inhomogeneous spin broadening. We demonstrate that a precise knowledge of this broadening is crucial both for a qualitative and a quantitative understanding of the temporal spin-cavity dynamics. On this basis we show that coherent oscillations between the spin ensemble and the cavity can be enhanced by a few orders of magnitude, when driving the system with pulses that match special resonance conditions. Our theoretical approach is tested successfully with an experiment based on an ensemble of negatively charged nitrogen-vacancy (NV) centers in diamond strongly coupled to a superconducting coplanar single-mode waveguide resonator.
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