Protecting a spin ensemble against decoherence in the strong-coupling regime of cavity QED

Abstract

Hybrid quantum systems based on spin ensembles coupled to superconducting microwave cavities are promising candidates for robust experiments in cavity quantum electrodynamics (QED) and for future technologies employing quantum mechanical e ects [1][2][3][4] . At present, the main source of decoherence in these systems is inhomogeneous spin broadening, which limits their performance for the coherent transfer and storage of quantum information [5][6][7] . Here we study the dynamics of a superconducting cavity strongly coupled to an ensemble of nitrogen-vacancy centres in diamond. We experimentally observe how decoherence induced by inhomogeneous broadening can be suppressed in the strong-coupling regime-a phenomenon known as 'cavity protection' 5,7 . To demonstrate the potential of this e ect for coherent-control schemes, we show how appropriately chosen microwave pulses can increase the amplitude of coherent oscillations between the cavity and spin ensemble by two orders of magnitude.The processing of quantum information requires special devices that can store and manipulate quantum bits. Hybrid quantum systems 2 combine the advantages of different systems to overcome their individual physical limitations. In this context superconducting microwave cavities have emerged as ideal tools for realizing strong coupling to qubits 3,4,[8][9][10][11][12] for the transfer of excitations on the singlephoton level 13,14 . For the storage of quantum information the negatively charged nitrogen-vacancy (NV) centres in diamond show great potential, especially owing to their long coherence times (up to one second 15 ) and to the combination of microwave and optical transitions which makes them an easily accessible and controllable qubit 16 . Coherently passing quantum information between such a spin and a cavity requires that they are strongly coupled to each other. As has recently been shown 4,10-12 , this limit can be reached by collective coupling to a large spin ensemble, in which case the coupling strength is increased by the square root of the ensemble size. However, this collective coupling comes with a considerable downside: in a solid-state environment a spin is always prone to inhomogeneous broadening. In particular, for an ensemble of NV centres, magnetic dipolar interaction with excess nuclear and electron spins in the diamond crystal leads to an inhomogeneous broadening of the spin transition 17 , which acts as the dominant source of decoherence. Several approaches, including echo-type refocusing techniques 18,19 , have been suggested to overcome this limitation. Here we will concentrate on recent theoretical proposals which rely on the specific shape of the inhomogeneous spectral In our homodyne detection measurements, the input microwave signal is split into two paths, both serving as a reference signal as well as for testing and controlling our experiment. Outside the cryostat both signal paths are combined by a frequency mixer and the quadratures I and Q are recorded with a fast analog-to-digital converter (ADC) ...

Optimal control of non-Markovian dynamics in a single-mode cavity strongly coupled to an inhomogeneously broadened spin ensemble

“…This form for ρ(ω) was established in our previous studies by a careful comparison with the experiment [29,36]. The right column shows that two holes were burnt into ρ(ω) at frequencies ωs ± Ω (two arrows in the inset) to suppress decoherence [26,27] Ω R ≈ 2Ω, and the total decoherence rate, Γ, mostly determined by the dephasing caused by the inhomogeneous broadening of the spin ensemble [36].…”

“…However, as was demonstrated in [26,29,37], the Volterra equation also governs quantum spin-cavity dynamics for the particular case when all spins are initially in the ground state and the cavity contains initially a single photon. Therefore, we take the amplitude of the write pulses, η (W ) |0/1 (t), such that the net power injected into the cavity corresponds to the power of a coherent driving signal with an amplitude equal to the cavity decay rate, κ.…”

“…1/2 [33], which leads to the enhancement of a single coupling strength, g j , by a factor of √ N (N ≈ 10 12 in [29]). We are aiming at the transfer of information from the cavity to the spin ensemble, its storage over a well-defined period of time, and its transfer back to the cavity.…”

Coherent Rabi Dynamics of a Superradiant Spin Ensemble in a Microwave Cavity

“…By varying M, we are able to control a delay in the onset of the superradiant emission [25] and we report the first experimental observation of a log dependence of this delay when the pseudospin is near quasiequilibrium at M ¼ S. This log dependence is consistent with predictions from the Tavis-Cummings model. We also observe an abrupt π-phase shift in the pseudospin microwave emission around this fully inverted state M ¼ S. Observations of the log dependence in the delay and the abrupt phase shift near full pseudospin inversion has eluded previous implementations of strongly coupled spin ensembles due to their much shorter T Ã 2 and the low fidelity of their pseudospin rotations (a direct consequence of nonuniform spin-cavity coupling) [26,27].…”

Detection of a weak magnetic field via cavity-enhanced Faraday rotation

“…Since the magnetic transition frequency of NV is about 2π × 2.8 GHz, we require a microwave cavity with ω r = 2π × 2.8 GHz. The decay rate γ of |m s = ±1 of the ground state triplet has been measured to vary from a few MHz [52,53] to 0.01Hz [54][55][56]. Our setup with practical parameters γ = 10 −3 κ i , κ ex = 10κ i and G = 0.1κ i , using a low-Q factor cross microstrip resonator with Q = 100 [41][42][43], yields κ i /2π = 28 MHz, and can provide a sensitivity of ∆B SP √ τ total 5.2 nT/ √ Hz for a single-photon probe field.…”