Analysis of quantum coherence in bismuth-doped silicon: A system of strongly coupled spin qubits

Mohammady, M. Hamed; Morley, Gavin W.; Nazir, Ahsan; Monteiro, T. S.

doi:10.1103/physrevb.85.094404

Cited by 37 publications

(57 citation statements)

References 40 publications

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“…More recently, systems with substantial electron-nuclear spin mixing have been attracting considerable attention, especially due to the presence of 'clock transitions' or 'optimal working points' (OWPs) where the qubit shows enhanced robustness to decoherence [14][15][16][17] and T 2 varies by orders of magnitude. A large number of important defects in the solid state possess such mixing, including donors in silicon, [18][19][20] NV centres in diamond, 21 transition metals in II-VI materials 22 and rare-earth dopants in silicates.…”

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confidence: 99%

Quantum-bath-driven decoherence of mixed spin systems

et al. 2014

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The decoherence of mixed electron-nuclear spin qubits is a topic of great current importance, but understanding is still lacking: while important decoherence mechanisms for spin qubits arise from quantum spin bath environments with slow decay of correlations, the only analytical framework for explaining observed sharp variations of decoherence times with magnetic field is based on the suppression of classical noise. Here we obtain a general expression for decoherence times of the central spin system which exposes significant differences between quantum-bath decoherence and decoherence by classical field noise. We perform measurements of decoherence times of bismuth donors in natural silicon using both electron spin resonance (ESR) and nuclear magnetic resonance (NMR) transitions, and in both cases find excellent agreement with our theory across a wide parameter range. The universality of our expression is also tested by quantitative comparisons with previous measurements of decoherence around 'optimal working points' or 'clock transitions' where decoherence is strongly suppressed. We further validate our results by comparison to cluster expansion simulations.

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Section: -13mentioning

confidence: 99%

Quantum-bath-driven decoherence of mixed spin systems

et al. 2014

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“…Therefore, examining the conditions for the validity of a classical Gaussian noise model is not only of fundamental interest but also highly desirable for accurate quantum control under realistic conditions. Bismuth donors in silicon (Si:Bi) have recently attracted much attention in spin-based quantum computation due to a number of favorable properties [18][19][20][21]. These include long electron spin coherence times of up to 3 s [22] observed for Bi donors (in isotopically enriched silicon-28) tuned to so-called clock transitions (CTs)-also known as optimal working points [23] or zero first-order Zeeman transitions)-whose frequency is insensitive, to first order, to magnetic field fluctuations.…”

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Classical nature of nuclear spin noise near clock transitions of Bi donors in silicon

Wolfowicz

et al. 2015

Phys. Rev. B

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Whether a quantum bath can be approximated as classical Gaussian noise is a fundamental issue in central spin decoherence and also of practical importance in designing noise-resilient quantum control. Spin qubits based on bismuth donors in silicon have tunable interactions with nuclear spin baths and are first-order insensitive to magnetic noise at so-called clock transitions (CTs). This system is therefore ideal for studying the quantum/classical Gaussian nature of nuclear spin baths since the qubit-bath interaction strength determines the back-action on the baths and hence the adequacy of a Gaussian noise model. We develop a Gaussian noise model with noise correlations determined by quantum calculations and compare the classical noise approximation to the full quantum bath theory. We experimentally test our model through a dynamical decoupling sequence of up to 128 pulses, finding good agreement with simulations and measuring electron spin coherence times approaching 1 s-notably using natural silicon. Our theoretical and experimental study demonstrates that the noise from a nuclear spin bath is analogous to classical Gaussian noise if the back-action of the qubit on the bath is small compared to the internal bath dynamics, as is the case close to CTs. However, far from the CTs, the back-action of the central spin on the bath is such that the quantum model is required to accurately model spin decoherence. Introduction. Central spin decoherence due to coupling to the environment is not only a central issue in understanding quantum-to-classical transitions [1,2], but also one of the key challenges in the realization of quantum computation [3]. There are two distinct models to describe the decoherence processes in such cases: in the semiclassical model, the central spin accumulates random phases due to thermal or quantum fluctuations of the environment [4,5], while in the quantum model, the coupling between the central spin and the environment produces entanglement and results in leakage of the which-way information from the central spin to the environment [6][7][8][9]. The fundamental difference between these two models lies in the fact that the classical noise is independent of the central spin state while the quantum noise is governed by the difference of environmental Hamiltonians conditioned on the qubit state, called the back-action from the central spin [10,11].The classical noise model of quantum baths, especially the Gaussian stochastic noise model, is a useful approximation in designing noise-resilient quantum control [12], which would otherwise require a large amount of numerical simulations of many-body dynamics of quantum baths. Dynamical decoupling has been employed to extract the noise spectra of baths [13][14][15][16][17], which are in turn used to design optimal quantum control for protecting quantum coherence and quantum gates. The viability of such methods critically

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“…By convention we will still refer to the |5, −1 ⇔ |4, −2 transition as allowed and the |5, −2 ⇔ |4, −1 transition as forbidden. These transitions were discussed by Mohammady et al who first pointed out their addressability based on microwave polarization 7 . Because these two transitions are between four distinct states, they can be used to form a two-qubit system.…”

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“…Bismuth donor electrons are particularly attractive because they have clock transitions which are first order insensitive to magnetic field noise [5][6][7][8][9] . This means that even in natural Si, electron spins can have long coherence times 5 .…”

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Addressing spin transitions onBi209donors in silicon using circularly polarized microwaves

et al. 2016

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Over the past decade donor spin qubits in isotopically enriched 28 Si have been intensely studied due to their exceptionally long coherence times. More recently bismuth donor electron spins have become popular because Bi has a large nuclear spin which gives rise to clock transitions (first-order insensitive to magnetic field noise). At every clock transition there are two nearly degenerate transitions between four distinct states which can be used as a pair of qubits. Here it is experimentally demonstrated that these transitions are excited by microwaves of opposite helicity such that they can be selectively driven by varying microwave polarization. This work uses a combination of a superconducting coplanar waveguide (CPW) microresonator and a dielectric resonator to flexibly generate arbitrary elliptical polarizations while retaining the high sensitivity of the CPW.Donors spins in Si are among the most promising quantum bits owing to their long coherence times (T 2 ) which exceed seconds in isotopically enriched 28 Si 1-4 . Bismuth donor electrons are particularly attractive because they have clock transitions which are first order insensitive to magnetic field noise [5][6][7][8][9] . This means that even in natural Si, electron spins can have long coherence times 5 . In Bi doped Si clock transitions come in pairs of nearly degenerate transitions separated by ∼1 MHz. These are predicted to be excited by microwaves of opposite circular polarization 7,10 . In this work we combine a coplanar waveguide microresonator (CPW) with a dielectric resonator to generate microwaves with tunable polarization. By varying this polarization, we demonstrate the selective addressability of the 7.03 GHz clock transitions. This will be important for hybrid donor-dot quantum computing schemes since the 5 GHz clock transition was recently predicted to form an avoided crossing with silicon based quantum dots 10 . This was discussed in the donor-dot surface code proposal by Pica et al 10 which also suggested addressing the clock transitions using microwave polarization.Bismuth donors in Si have a large hyperfine coupling which not only gives rise to a large zero field splitting, but also allows for rapid manipulation of both the electronic and nuclear spin states when operating in the intermediate field regime where the hyperfine coupling is comparable to the Zeeman splitting 8,[11][12][13] . In this regime we describe the states using the total spin, F , and its projection, m F 6 . The total spin is given by F = I ± S where I is the nuclear spin and S is the electron spin. At the 7.03 GHz clock transition the two nearly degenerate transitions are described in the |F, m F basis by |5, −1 ⇔ |4, −2 and |5, −2 ⇔ |4, −1 . In the high field limit the second transition is forbidden since it involves a nuclear spin flip, but due to strong mixing, both transitions are accessible near the clock transition. By convention we will still refer to the |5, −1 ⇔ |4, −2 transition as allowed and the |5, −2 ⇔ |4, −1 transition as forbidden. These transi...

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Analysis of quantum coherence in bismuth-doped silicon: A system of strongly coupled spin qubits

Cited by 37 publications

References 40 publications

Quantum-bath-driven decoherence of mixed spin systems

Quantum-bath-driven decoherence of mixed spin systems

Classical nature of nuclear spin noise near clock transitions of Bi donors in silicon

Addressing spin transitions onBi209donors in silicon using circularly polarized microwaves

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