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arXiv:1203.4631 · Physical Review A

Protecting and enhancing spin squeezing via continuous dynamical decoupling

Adam Zaman Chaudhry, Jiangbin Gong

Published Jul 13, 2012• 25 citations
arXivHTMLPDF

Abstract

Realizing useful quantum operations with high fidelity is a two-task quantum control problem wherein decoherence is to be suppressed and desired unitary evolution is to be executed. The dynamical decoupling (DD) approach to decoherence suppression has been fruitful but synthesizing DD fields with certain quantum control fields may be experimentally demanding. In the context of spin squeezing, here we explore an unforeseen possibility that continuous DD fields may serve dual purposes at once. In particular, it is shown that a rather simple configuration of DD fields can suppress collective decoherence and yield a $1/N$ scaling of the squeezing performance ($N$ is the number of spins), thus making spin squeezing more robust to noise and much closer to the so-called Heisenberg limit. The theoretical predictions should be within the reach of current spin squeezing experiments.

DOI
10.1103/physreva.86.012311

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Realizing useful quantum operations with high fidelity is a two-task quantum control problem wherein decoherence is to be suppressed and desired unitary evolution is to be executed. The dynamical decoupling (DD) approach to decoherence suppression has been fruitful but synthesizing DD fields with certain quantum control fields may be experimentally demanding. In the context of spin squeezing, here we explore an unforeseen possibility that continuous DD fields may serve dual purposes at once. In particular, it is shown that a rather simple configuration of DD fields can suppress collective decoherence and yield a 1/N1/N1/N scaling of the squeezing performance (NNN is the number of spins), thus making spin squeezing more robust to noise and much closer to the so-called Heisenberg limit. The theoretical predictions should be within the reach of current spin squeezing experiments.
Introduction and overview As mentioned in Chapter 4, dynamical decoupling (DD) techniques have developed decades of tradition in the context of NMR spectroscopy, where they continue to play a pervasive role throughout all aspects of imaging and coherent control of multi-spin dynamics in the liquid and solid state. A dedicated experimental characterization and exploitation of DD as a tool for high-fidelity dynamical control and decoherence suppression in different quantum information processing (QIP) platforms has been undertaken only in more recent years, largely enabled by impressive laboratory progress in fast and ultrafast coherent control capabilities over the past decade. Without attempting to provide a comprehensive in-depth account, it is our goal in this chapter to highlight some key experimental advances to illustrate the significance of DD strategies for near-term practical quantum error control in QIP; and justify why, quoting from a recent experimental work [MTA+06], they “will likely form a quintessential element in real quantum computers.” The large majority of dynamical error-suppression implementations in QIP have aimed thus far to validate DD as a tool for enhanced quantum memory in different qubit devices in the presence of various decoherence mechanisms. Likewise, with the exception of a recent work reporting the suppression of collisional decoherence using a “continuous spin echo” close in spirit to Eulerian DD [SAD10], the majority of experiments have employed (sufficiently) “hard” pulses, such that any evolution other than that due to the control field could be taken as negligible and the bang-bang (BB) limit formalized in Chapter 4 invoked as an adequate approximation.
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Dynamical decoupling (DD) is an active and effective method for suppressing decoherence of a quantum system from its environment. In contrast to the nominal biaxial DD, this work presents a uniaxial decoupling protocol that requires a significantly reduced number of pulses and a much lower bias field satisfying the "magic" condition. We show this uniaxial DD protocol works effectively in a number of model systems of practical interest, e.g., a spinor atomic Bose-Einstein condensate in stray magnetic fields (classical noise), or an electron spin coupled to nuclear spins (quantum noise) in a semiconductor quantum dot. It requires only half the number of control pulses and a 10-100 times lower bias field for decoupling as normally employed in the above mentioned illustrative examples, and the overall efficacy is robust against rotation errors of the control pulses. The uniaxial DD protocol we propose shines new light on coherent controls in quantum computing and quantum information processing, quantum metrology, and low field nuclear magnetic resonance.
In quantum information processing, it is vital to protect the coherence of qubits in noisy environments. Dynamical decoupling (DD), which applies a sequence of flips on qubits and averages the qubit-environment coupling to zero, is a promising strategy compatible with other desired functionalities, such as quantum gates. Here, we review the recent progresses in theories of dynamical decoupling and experimental demonstrations. We give both semiclassical and quantum descriptions of the qubit decoherence due to coupling to noisy environments. Based on the quantum picture, a geometrical interpretation of DD is presented. The periodic Carr-Purcell-Meiboom-Gill DD and the concatenated DD are reviewed, followed by a detailed exploration of the recently developed Uhrig DD, which employs the least number of pulses in an unequally spaced sequence to suppress the qubit-environment coupling to a given order of the evolution time. Some new developments and perspectives are also discussed.
Dephasing--phase randomization of a quantum superposition state--is a major obstacle for the realization of high fidelity quantum logic operations. Here, we implement a two-qubit controlled-NOT gate using dynamical decoupling (DD), despite the gate time being more than 1 order of magnitude longer than the intrinsic coherence time of the system. For realizing this universal conditional quantum gate, we have devised a concatenated DD sequence that ensures robustness against imperfections of DD pulses that otherwise may destroy quantum information or interfere with gate dynamics. We compare its performance with three other types of DD sequences. These experiments are carried out using a well-controlled prototype quantum system--trapped atomic ions coupled by an effective spin-spin interaction. The scheme for protecting conditional quantum gates demonstrated here is applicable to other physical systems, such as nitrogen vacancy centers, solid state nuclear magnetic resonance, and circuit quantum electrodynamics.