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arXiv:1706.07876 · Physical Review A

Synthetic clock transitions via continuous dynamical decoupling

Dimitrios Trypogeorgos, Ana Valdés-Curiel, Nathan E. Lundblad, Ian B. Spielman

Published Jan 16, 2018• 36 citations
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Abstract

Decoherence of quantum systems due to uncontrolled fluctuations of the environment presents fundamental obstacles in quantum science. Clock transitions which are insensitive to such fluctuations are used to improve coherence, however, they are not present in all systems or for arbitrary system parameters. Here we create a trio of synthetic clock transitions using continuous dynamical decoupling in a spin-1 Bose-Einstein condensate in which we observe a reduction of sensitivity to magnetic-field noise of up to four orders of magnitude; this work complements the parallel work by Anderson et al. [R. P. Anderson et al., following paper, Phys. Rev. A 97, 013408 (2018)]. In addition, using a concatenated scheme, we demonstrate suppression of sensitivity to fluctuations in our control fields. These field-insensitive states represent an ideal foundation for the next generation of cold-atom experiments focused on fragile many-body phases relevant to quantum magnetism, artificial gauge fields, and topological matter.

DOI
10.1103/physreva.97.013407

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Decoherence of quantum systems due to uncontrolled fluctuations of the environment presents fundamental obstacles in quantum science. Clock transitions which are insensitive to such fluctuations are used to improve coherence, however, they are not present in all systems or for arbitrary system parameters. Here we create a trio of synthetic clock transitions using continuous dynamical decoupling in a spin-1 Bose-Einstein condensate in which we observe a reduction of sensitivity to magnetic-field noise of up to four orders of magnitude; this work complements the parallel work by Anderson et al. [R. P. Anderson et al., following paper, Phys. Rev. A 97, 013408 (2018)]. In addition, using a concatenated scheme, we demonstrate suppression of sensitivity to fluctuations in our control fields. These field-insensitive states represent an ideal foundation for the next generation of cold-atom experiments focused on fragile many-body phases relevant to quantum magnetism, artificial gauge fields, and topological matter.
We present a novel continuous dynamical decoupling scheme for the construction of a robust qubit in a three-level system. By means of a clock transition adjustment, we first show how robustness to environmental noise is achieved, while eliminating drive-noise, to first-order. We demonstrate this scheme with the spin sub-levels of the NV-centre's electronic ground state. By applying drive fields with moderate Rabi frequencies, the drive noise is eliminated and an improvement of 2 orders of magnitude in the coherence time is obtained compared to the pure dephasing time. We then show how the clock transition adjustment can be tuned to eliminate also the second-order effect of the environmental noise with moderate drive fields. A further detailed theoretical investigation suggests an additional improvement of more than 1 order of magnitude in the coherence time which is supported by simulations. Hence, our scheme predicts that the coherence time may be prolonged towards the lifetime-limit using a relatively simple experimental setup.
The loss of coherence is one of the main obstacles for the implementation of quantum information processing. The efficiency of dynamical decoupling schemes, which have been introduced to address this problem, is limited itself by the fluctuations in the driving fields which will themselves introduce noise. We address this challenge by introducing the concept of concatenated continuous dynamical decoupling, which can overcome not only external magnetic noise but also noise due to fluctuations in driving fields. We show theoretically that this approach can achieve relaxation limited coherence times, and demonstrate experimentally that already the most basic implementation of this concept yields an order of magnitude improvement to the decoherence time for the electron spin of nitrogen vacancy centers in diamond. The proposed scheme can be applied to a wide variety of other physical systems, including trapped atoms and ions and quantum dots, and may be combined with other quantum technologies challenges such as quantum sensing and quantum information processing.
We present a novel continuous dynamical decoupling scheme for the construction of a robust qubit in a three-level system. By means of a clock transition adjustment, we first show how robustness to environmental noise is achieved, while eliminating drive-noise, to first-order. We demonstrate this scheme with the spin sub-levels of the NV-centre's electronic ground state. By applying drive fields with moderate Rabi frequencies, the drive noise is eliminated and an improvement of 2 orders of magnitude in the coherence time is obtained compared to the pure dephasing time. We then show how the clock transition adjustment can be tuned to eliminate also the second-order effect of the environmental noise with moderate drive fields. A further improvement of more than 1 order of magnitude in the coherence time is expected and confirmed by simulations. Hence, our scheme prolongs the coherence time towards the lifetime-limit using a relatively simple experimental setup.
We analyze the robust character against the nonstatic noise of clock transitions implemented via a method of continuous dynamical decoupling (CDD) in a hyperfine Zeeman multiplet in 87Rb^{87}\mathrm{Rb}87Rb. The emergence of features specific to the quadratic corrections to the linear Zeeman effect is evaluated. Our analytical approach, which combines methods of stochastic analysis with time-dependent perturbation theory, allows tracing the deco- herence process for generic noise sources. Working first with a basic CDD scheme, it is shown that the amplitude and frequency of the (sinusoidal driving) field of control can be appropriately chosen to force the nonstatic random input to have a (time-dependent) perturbative character. Moreover, in the dressed-state picture, the effect of noise is described in terms of an operative random variable whose properties, dependent on the driving field, can be analytically characterized. In this framework, the relevance of the spectral density of the fluctuations to the performance of the CDD technique is precisely assessed. In particular, the range of noise correlation times where the method of decoherence reduction is still efficient is identified. The results obtained in the basic CDD framework are extrapolated to concatenated schemes. The generality of our approach allows its applicability beyond the specific atomic system considered.
We present the experimental realization of a continuous dynamical decoupling scheme which suppresses leading frequency shifts in a multi-ion frequency reference based on 40Caþ. By near-resonant magnetic coupling of the 2S1=2 and 2D5=2 Zeeman sublevels using radio-frequency dressing fields, engineered transitions with reduced sensitivity to magnetic-field fluctuations are obtained. A second stage detuned dressing field reduces the influence of amplitude noise in the first stage driving fields and decreases 2nd-rank tensor shifts, such as the electric quadrupole shift. Suppression of the quadratic dependence of the quadrupole shift to 3ð2Þ mHz=μm2 and coherence times of 290(20) ms on the optical transition are demonstrated even within a laboratory environment with significant magnetic field noise. Besides removing inhomogeneous line shifts in multi-ion clocks, the demonstrated dynamical decoupling technique may find applications in quantum computing and simulation with trapped ions by a tailored design of decoherence-free subspaces.
We present the experimental realization of a continuous dynamical decoupling scheme which suppresses leading frequency shifts in a multi-ion frequency reference based on 40Ca+^{40}\mathrm{Ca}^+40Ca+. By near-resonant magnetic coupling of the 2S1/2^2\mathrm{S}_{1/2}2S1/2​ and 2D5/2^2\mathrm{D}_{5/2}2D5/2​ Zeeman sub-levels using radio-frequency dressing fields, engineered transitions with reduced sensitivity to magnetic-field fluctuations are obtained. A second stage detuned dressing field reduces the influence of amplitude noise in the first stage driving fields and decreases 2\textsuperscript{nd}-rank tensor shifts, such as the electric quadrupole shift. Suppression of the quadratic dependence of the quadrupole shift to 3(2) mHz/μm23(2)\,\text{mHz}/μm^23(2)mHz/μm2 and coherence times of 290(20) ms290(20)\,\text{ms}290(20)ms on the optical transition are demonstrated even within a laboratory environment with significant magnetic field noise. Besides removing inhomogeneous line shifts in multi-ion clocks, the demonstrated dynamical decoupling technique may find applications in quantum computing and simulation with trapped ions by a tailored design of decoherence-free subspaces.