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arXiv:2005.03908 · Physical Review Applied

Estimation of the Laser Frequency Noise Spectrum by Continuous Dynamical Decoupling

Manchao Zhang, Yi Xie, Jie Zhang, Weichen Wang, Chun-Wang Wu, Ting Chen, Wei Wu, Ping‐Xing Chen

Published Jan 20, 2021• 8 citations
arXivHTMLPDF

Abstract

Decoherence induced by laser frequency noise is one of the most important obstacles in quantum information processing. In order to suppress this decoherence, the noise power spectral density needs to be accurately characterized. In particular, the noise spectrum measurement based on the coherence characteristics of qubits would be a meaningful and still challenging method. Here, we theoretically analyze and experimentally obtain the spectrum of laser frequency noise based on the continuous dynamical decoupling technique. We first estimate the mixture-noise (including laser and magnetic noises) spectrum up to $(2\ensuremath{\pi})530$ kHz by monitoring the transverse relaxation from an initial state $+X$, followed by a gradient descent data process protocol. Then the contribution from the laser noise is extracted by encoding the qubits on different Zeeman sublevels. We also investigate two sufficiently strong noise components by making an analogy between these noises and driving lasers whose linewidth is assumed to be negligible. This method is verified experimentally and finally helps to characterize the noise.

DOI
10.1103/physrevapplied.15.014033

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Decoherence induced by laser frequency noise is one of the most important obstacles in quantum information processing. In order to suppress this decoherence, the noise power spectral density needs to be accurately characterized. In particular, the noise spectrum measurement based on the coherence characteristics of qubits would be a meaningful and still challenging method. Here, we theoretically analyze and experimentally obtain the spectrum of laser frequency noise based on the continuous dynamical decoupling technique. We first estimate the mixture-noise (including laser and magnetic noises) spectrum up to (2\ensuremathπ)530(2\ensuremath{\pi})530(2\ensuremathπ)530 kHz by monitoring the transverse relaxation from an initial state +X+X+X, followed by a gradient descent data process protocol. Then the contribution from the laser noise is extracted by encoding the qubits on different Zeeman sublevels. We also investigate two sufficiently strong noise components by making an analogy between these noises and driving lasers whose linewidth is assumed to be negligible. This method is verified experimentally and finally helps to characterize the noise.
Decoherence is one of the most important obstacles that must be overcome in quantum information processing. It depends on the qubit-environment coupling strength, but also on the spectral composition of the noise generated by the environment. If the spectral density is known, fighting the effect of decoherence can be made more effective. Applying sequences of inversion pulses to the qubit system, we developed a method for dynamical decoupling noise spectroscopy. We generate effective filter functions that probe the environmental spectral density without requiring assumptions about its shape. Comparing different pulse sequences, we recover the complete spectral density function and distinguish different contributions to the overall decoherence.
Characterizing and understanding noise affecting quantum states has immense benefits in spectroscopy as well as in realizing quantum devices. Transverse relaxation times under a set of dynamical decoupling (DD) sequences with varying interpulse delays were earlier used for obtaining the noise spectral densities of single-qubit coherences. In this work, using a pair of homonuclear spins and NMR techniques, we experimentally characterize noise in certain decoherence-free subspaces. We also explore the noise of similar states in a heteronuclear spin pair. Further, using a 10-qubit system, we investigate noise profiles of various multiqubit coherences and study the scaling of noise with respect to the coherence order. Finally, using the experimentally obtained noise spectrum of the 10-qubit NOON state, we predict the performance of a Uhrig DD sequence and verify it experimentally.
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.
I present a theory of environmental noise spectroscopy via dynamical decoupling of a qubit at an optimal working point. Considering a sequence of nnn pulses and pure dephasing due to quadratic coupling to Gaussian distributed noise $\ensuremath{\xi}(t)$, I use the linked-cluster (cumulant) expansion to calculate the coherence decay. Solutions allowing for reconstruction of spectral density of noise are given. For noise with correlation time shorter than the time scale on which coherence decays, the noise filtered by the dynamical decoupling procedure can be treated as effectively Gaussian at large nnn, and well-established methods of noise spectroscopy can be used to reconstruct the spectrum of ${\ensuremath{\xi}}^{2}(t)$ noise. On the other hand, for noise of dominant low-frequency character $(1/{f}^{\ensuremath{\beta}}$ noise with $\ensuremath{\beta}>1)$, an infinite-order resummation of the cumulant expansion is necessary, and it leads to an analytical formula for coherence decay having a power-law tail at long times. In this case, the coherence at time ttt depends both on spectral density of $\ensuremath{\xi}(t)$ noise at $\ensuremath{\omega}=n\ensuremath{\pi}/t$, and on the effective low-frequency cutoff of the noise spectrum, which is typically given by the inverse of the data acquisition time. Simulations of decoherence due to purely transverse noise show that the analytical formulas derived in this paper apply in this often encountered case of an optimal working point, provided that the number of pulses is not very large, and that the longitudinal qubit splitting is much larger than the transverse noise amplitude.
Abstract Magnetic field noise is an important factor causing quantum decoherence in quantum systems. In order to suppress the decoherence effect, magnetic field noise needs to be properly measured and controlled. Magnetic field noise power spectrum measurement using a single trapped ion based quantum spectrum analyzer is a very effective way. In this paper, the magnetic field noise measurement based on dynamic decoupling technique is analyzed theoretically. Furthermore, we use magnetically insensitive transition to measure the magnetic field noise, which has the potential to measure stronger magnetic field noise and speed up the measurement process. In our experiment, we suppress the magnetic field noise by using active feedback control and passive compensation, where the required passive compensation amplitude is obtained by measuring the magnetic field noise spectrum of a single 25Mg+ ion. With the magnetic field noise suppressed, the expected contribution of the magnetic field noise to the stability of the 25Mg+–27Al+ ion optical clock can be decreased from 2.8 × 1 0 − 15 / τ to 7.2 × 1 0 − 16 / τ .
With the power of chemistry for inexpensive synthesis of tailored systems, molecular qubits are attractive candidates for quantum computing. Here decoherence persists as a major obstacle; for its effective suppression, the properties of environmental noise must be elucidated. Traditional noise spectroscopy with spurious harmonics leads to false identification of nuclear spins. The authors demonstrate a protocol for noise-spectrum analysis without spurious harmonics, through dynamical decoupling. This result enables enhanced coherence for molecular qubits, and could be quite significant for quantum information processing based on such systems.