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Journal of Physics B Atomic Molecular and Optical Physics

Suppression of error in qubit rotations due to Bloch–Siegert oscillation via the use of off-resonant Raman excitation

Prabhakar Pradhan, George C. Cardoso, M. S. Shahriar

Published Mar 9, 2009• 4 citations
Publisher

Abstract

The rotation of a quantum bit (qubit) is an important step in quantum computation. The rotation is generally performed using a Rabi oscillation. In a direct two-level qubit system, if the Rabi frequency is comparable to its resonance frequency, the rotating wave approximation is not valid, and the Rabi oscillation is accompanied by the so-called Bloch–Siegert oscillation (BSO) that occurs at twice the frequency of the driving field. One implication of the BSO is that for a given interaction time and Rabi frequency, the degree of rotation experienced by the qubit depends explicitly on the initial phase of the driving field. If this effect is not controlled, it leads to an apparent fluctuation in the rotation of the qubit. Here we show that when an off-resonant lambda system is used to realize a two-level qubit, the BSO is inherently negligible, thus eliminating this source of potential error.

DOI
10.1088/0953-4075/42/6/065501

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The rotation of a quantum bit (qubit) is an important step in quantum computation. The rotation is generally performed using a Rabi oscillation. In a direct two-level qubit system, if the Rabi frequency is comparable to its resonance frequency, the rotating wave approximation is not valid, and the Rabi oscillation is accompanied by the so-called Bloch–Siegert oscillation (BSO) that occurs at twice the frequency of the driving field. One implication of the BSO is that for a given interaction time and Rabi frequency, the degree of rotation experienced by the qubit depends explicitly on the initial phase of the driving field. If this effect is not controlled, it leads to an apparent fluctuation in the rotation of the qubit. Here we show that when an off-resonant lambda system is used to realize a two-level qubit, the BSO is inherently negligible, thus eliminating this source of potential error.
In a direct two-level qubit system, when the Rabi frequency is comparable to the resonance frequency, the rotating wave approximation is not appropriate. In this case, the Rabi oscillation is accompanied by another oscillation at twice the frequency of the driving field, the so called Bloch-Siegert oscillation (BSO), which depends on the initial phase of the driving field. This oscillation may restrict the precise rotation of a qubit made of direct two-level system. Here, we show that in case of an effectively two-level lambda system, the BSO is inherently negligible, implying a greater precision for rotation of a qubit made of such a lambda system when compared to a direct two-level qubit in a strong driving field.
The need to maximize the number of operations of a quantum bit within its decoherence time may require the ratio of Rabi frequency to transition frequency to be large enough to invalidate the rotating-wave approximation. The state of the quantum bit under any initial condition then depends explicitly on the phase of the driving field, resulting in driver-phase-correlated fluctuations and a violation of the rule that the degree of excitation depends only on the pulse area. This is due to the interference of the excitations caused by the corotating and counterrotating fields, and is a significant source of error, correctable only by controlling the driver phase. We present a scheme for observing this effect under currently realizable parameters.
Rabi oscillations describe the coherent evolution of a two-level quantum system under the influence of a resonant driving field. They are central to quantum computing and determine the utility of qubits. Reliable control of these oscillations requires precise calibration of the driving field; however, experimental implementations are subject to imperfections that stray from what is ideal. One source of error is amplitude miscalibration, where the strength of the applied control pulse fluctuates around its intended value.In this study, the effects of amplitude error on Rabi oscillations were investigated using a formulaic simulation of a single-qubit system. The system was modeled using the Cirq quantum circuit framework, where Rabi oscillations were represented as rotations on the Bloch sphere. Amplitude divergence was incorporated by modifying the Rabi drive strength with Gaussian-distributed noise. The resulting state evolution was compared with the ideal theoretical oscillation in order to visualize the impact of stochastic amplitude variations on qubit dynamics.This model provides a simplified framework for examining how imperfect calibration influences coherent quantum state evolution in two-level systems.
We present investigations of radio-frequency (RF) resonances observed in an optically pumped rubidium vapor. By measuring the systematic shifts (the Bloch–Siegert shifts) of RF resonances in low magnetic fields, we demonstrate limitations of the rotating-wave approximation in the case of angular momentum F ≥ 1. The resonance shifts and deformations are characterized in a wide range of parameters and it is shown that the observed behavior is far more complex than in a standard two-level system. It is also demonstrated that the shifts can be controllably turned on or off by switching between the oscillating and rotating magnetic field. Experimental results are supported with numerical calculations, reproducing all features of the observed signals. Besides fundamental aspect of the research, application of rotating magnetic field helps to suppress/evaluate spectroscopic-measurement and precise-metrology systematic errors. The reported study has also important implications for quantum metrology and information processing beyond RWA and standard two-state qubit dynamics.
Abstract We study the coherent dynamics of a qubit excited by an amplitude-modulated electromagnetic field under the Rabi resonance when the frequency of the low-frequency modulation field matches the Rabi frequency in the high-frequency field. Due to the destructive interference of multiple photon processes within the ultrastrong coupling between the qubit and the low-frequency driving field, Rabi oscillations result exclusively from the Bloch–Siegert effect. It is directly observed in the time-resolved coherent dynamics as the Bloch–Siegert oscillation. In this case, triplets in the Fourier spectra of the coherent response are transformed into doublets with the splitting between the lines equal to twice the Bloch–Siegert shift. These unusual properties are demonstrated in the conditions of experiments with a nitrogen vacancy center in the diamond.