Echo Trains in Pulsed Electron Spin Resonance of a Strongly Coupled Spin Ensemble

Weichselbaumer, Stefan; Zens, Matthias; Zollitsch, Christoph W.; Brandt, Martin S.; Rotter, Stefan; Gross, Rudolf; Huebl, Hans

doi:10.1103/physrevlett.125.137701

Cited by 21 publications

(25 citation statements)

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“…A similar result was reported recently in Ref. [33], which showed that the secondary echoes were absent when the light-matter coupling was reduced. Indeed, secondary echoes were discerned in the very first microwave spin echo experiment in 1958 [34], where highly doped samples were used to compensate low detector sensitivity.…”

supporting

confidence: 91%

“…Future efforts shall be devoted to understand the scaling laws that govern the gradual reduction of the self-stimulated echo amplitudes, and how these depend on the spin and cavity parameters. It is evident from the present study that in addition to the cavity linewidth and the spin dephasing rates [33], this decay will also depend nonlinearly on the intensity of the echoes, e.g., due to the incomplete refocusing by previous echoes, and the total number of spins effectively coupled to the resonator. Other factors such as the distribution of detunings and coupling strengths may offer varying contribution to the precise behavior of this decay.…”

mentioning

confidence: 80%

“…Following Ref. [33], in Fig. 2(d), we plot the emitted photon number in each echo A echo ¼ R echo jαj 2 κdt as a function of its order of emission from both experiments and numerical calculations with τ ¼30μs and Γ ¼ 2π × 2.5 kHz.…”

mentioning

confidence: 99%

“…Although the secondary echoes studied here may constitute an unavoidable feature to be mitigated in quantum memory or transducer protocols involving spin ensembles, they may also offer opportunities in ESR spectroscopy. Aside from the potential to improve signal-to-noise by averaging multiple echoes in one train, these secondary echoes could provide an efficient route to obtaining information on loss rates in the system [33] or reveal spectroscopic information, for example in more complex spin systems with unresolved hyperfine couplings. The understanding and theoretical framework that we present here forms a basis to explore such opportunities in more detail.…”

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confidence: 99%

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Self-Stimulated Pulse Echo Trains from Inhomogeneously Broadened Spin Ensembles

et al. 2020

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We show experimentally and describe theoretically how a conventional magnetic resonance Hahn echo sequence can lead to a self-stimulated pulse echo train when an inhomogeneously broadened spin ensemble is coupled to a resonator. Effective strong coupling between the subsystems assures that the first Hahn echo can act as a refocusing pulse on the spins, leading to self-stimulated secondary echoes. Within the framework of mean field theory, we show that this process can continue multiple times leading to a train of echoes. We introduce an analytical model that explains the shape of the first echo and numerical results that account well for the experimentally observed shape and strength of the echo train and provides insights into the collective effects involved.

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confidence: 91%

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confidence: 80%

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confidence: 99%

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confidence: 99%

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Self-Stimulated Pulse Echo Trains from Inhomogeneously Broadened Spin Ensembles

et al. 2020

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“…In a cavity containing N coherent spins with homogeneous single-spin coupling, g 0 , the ensemble coupling strength, g ens becomes enhanced through collective coupling: g ens = g 0 √ N , [7]. A variety of paramagnetic spin ensembles with spin concentrations of 10 17−20 cm −3 have already been used to demonstrate high-cooperativity coupling to planar superconducting resonators [8][9][10][11]. For example, using phosphorus donors in isotopically purified silicon, C ∼ 2 has been achieved; however, the coherence time, T 2 , in that experiment was limited to only approximately 2 ms, despite coherence times approaching seconds being measured in the same spin system in the dilute limit and in the bulk [12].…”

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confidence: 99%

Spin-Resonance Linewidths of Bismuth Donors in Silicon Coupled to Planar Microresonators

et al. 2020

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Ensembles of bismuth-donor spins in silicon are promising storage elements for microwave quantum memories due to their long coherence times, which exceed seconds. The operation of an efficient quantum memory requires the achievement of critical coupling between the spin ensemble and a suitable highquality factor resonator-this in turn requires a thorough understanding of the line shapes for the relevant spin-resonance transitions, particularly considering the influence of the resonator itself on line broadening. Here, we present pulsed electron-spin-resonance measurements of ensembles of bismuth donors in natural silicon, above which niobium superconducting resonators have been patterned. By studying spin transitions across a range of frequencies and fields, we identify distinct line-broadening mechanisms and, in particular, those that can be suppressed by operating at magnetic-field-insensitive "clock transitions." Given the donor concentrations and resonator used here, we measure a cooperativity C ∼ 0.2 and based on our findings we discuss a route to achieve unit cooperativity, as required for a quantum memory.

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Room‐Temperature Quantum Memories Based on Molecular Electron Spin Ensembles

et al. 2021

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Superconducting quantum bits are addressed by means of microwave radiation and quantum memories in this context thus need to be able to store microwave photon states. To this end, resonant structures for electromagnetic radiation can be used to strongly couple quantum bits and quantum memories to quantized cavity modes of the electromagnetic field. The strong coupling generates a hybrid quantum system that allows mapping the qubit state onto the cavity field state. [6] This strategy has given rise to the field of cavity quantum electrodynamics and has already been used to couple two superconducting qubits together via a cavity bus. [7] A second application of quantum memories is in quantum repeaters for quantum communication. Because telecom wavelengths are in the near-infrared, for this application, optical quantum memories are required that store optical photon states. [8] Considering the choice of material platform for designing microwave quantum memories, electron spins in solids can be easily addressed by microwave pulses and have been shown to possess excellent coherence times up to seconds, for some systems even up to room temperature. [9][10] Unfortunately, the coupling of a single electron spin to a photon is very weak. Although resonant structures can be tailored to improve single-spin coupling, [11][12][13] the weakness of the coupling renders addressing individual spins by means of coupling to cavity modes very challenging. This can be overcome by using an electron spin ensemble rather than single spins, because the coupling strength of a spin ensemble to an electromagnetic resonator mode is proportional to the square root of the number of electron spins in the ensemble. [14] This then leads to the general idea of the implementation of a microwave quantum memory using spin ensembles and microwave resonators (Figure 1). The state to be stored is encoded in a weak microwave pulse and sent to the hybrid quantum system constituted of an electron spin ensemble that is strongly coupled to a microwave resonator, where it is stored. When the quantum state is needed again, a strong microwave pulse is sent to the resonator, which leads to deterministic retrieval of the quantum state that is emitted as a microwave photon to be used as desired.Strong coupling between cavity and electron spin ensembles has been observed in a variety of spin systems, including organic radicals, [15][16][17][18][19][20] phosphorous dopants in silicon, [21,22] P1 and nitrogen vacancy (NV) defects in diamond, [23][24][25][26][27][28][29][30][31][32] N@ C 60 , [33] rare earth dopants in oxides, [34,35] transition metal Whilst quantum computing has recently taken great leaps ahead, the development of quantum memories has decidedly lagged behind. Quantum memories are essential devices in the quantum technology palette and are needed for intermediate storage of quantum bit states and as quantum repeaters in long-distance quantum communication. Current quantum memories operate at cryogenic, mostly sub-Kelvin temperatures and require extens...

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Echo Trains in Pulsed Electron Spin Resonance of a Strongly Coupled Spin Ensemble

Cited by 21 publications

References 66 publications

Self-Stimulated Pulse Echo Trains from Inhomogeneously Broadened Spin Ensembles

Self-Stimulated Pulse Echo Trains from Inhomogeneously Broadened Spin Ensembles

Spin-Resonance Linewidths of Bismuth Donors in Silicon Coupled to Planar Microresonators

Room‐Temperature Quantum Memories Based on Molecular Electron Spin Ensembles

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