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Physical Review A

Quantum beats for the measurement of topological phases in Rabi oscillations of two-level atoms

G. S. Agarwal

Published Dec 1, 1988• 9 citations
Publisher

Abstract

We demonstrate how the topological phase associated with Rabi flopping in two-level atoms in optical fields can be measured by quantum-beat experiments. We use the Zeeman coherences in $j=0$ to $j=1$ transition which is excited by both broad-band field and circularly polarized pulses.

DOI
10.1103/physreva.38.5957

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Motivated by the recent experimental work (A. Widera, \textit{et al}, Phys. Rev. Lett. 95, 19045), we study the collisional spin dynamics of two spin-2 $% ^{87}$Rb atoms confined in a deep optical lattice. When the system is initialized as $|0,0>$, three different two-particle Zeeman states are involved in the time evolution due to the conservation of magnetization. For a large magnetic field $B>0.8$ Guass, the spin coherent dynamics reduces to a Rabi-like oscillation between the states $|0,0>$ and $% |1,-1>$. However, under a small magnetic field, a general three-level coherent oscillation displays. In particular, around a critical magnetic field $B_{c}\simeq 0.48$ Guass, the probability in the Zeeman states $% |2,-2> $ exhibits a novel quantum beat phenomenon, ready to be confirmed in future experiments.

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Physical Review A•Sep 1, 1993•72 citations
We demonstrate how the topological phase associated with Rabi flopping in two-level atoms in optical fields can be measured by quantum-beat experiments. We use the Zeeman coherences in j=0j=0j=0 to j=1j=1j=1 transition which is excited by both broad-band field and circularly polarized pulses.
Quantum beat phenomenon presence in coherent spin dynamics of spin-2 87^{87}87Rb atoms in a deep optical lattice
Motivated by the recent experimental work (A. Widera, \textit{et al}, Phys. Rev. Lett. 95, 19045), we study the collisional spin dynamics of two spin-2 % ^{87}Rb atoms confined in a deep optical lattice. When the system is initialized as ∣0,0>|0,0>∣0,0>, three different two-particle Zeeman states are involved in the time evolution due to the conservation of magnetization. For a large magnetic field B>0.8B>0.8B>0.8 Guass, the spin coherent dynamics reduces to a Rabi-like oscillation between the states ∣0,0>|0,0>∣0,0> and % |1,-1>. However, under a small magnetic field, a general three-level coherent oscillation displays. In particular, around a critical magnetic field Bc≃0.48B_{c}\simeq 0.48Bc​≃0.48 Guass, the probability in the Zeeman states $% |2,-2> $ exhibits a novel quantum beat phenomenon, ready to be confirmed in future experiments.
A commonly observed quantum-interference phenomenon is Rabi oscillations—understood as a ‘quantum beat’ between two dressed states separated by the Rabi splitting (RS) energy in a driven two-level (artificial) atom [1]. It is a signature of quantum coherence fundamental to the manipulation of atomic qubits in quantum information processing, and has been observed in quantum dots (QDs) (see Ref [2] and references therein). Another quantum-beat phenomenon occurs due to interference between the excited states of a V-type atomic system and has also been observed in the transient decay of QD emission from a suddenly excited neutral exciton state X0—an effective V-type system due to fine-structure splitting (FSS). Despite much related theoretical work and the availability of various platforms in which V-type systems could be realised, the observation of Rabi oscillations in resonance fluorescence from a coherently driven three-level V-type system remains a fundamentally interesting open question. In particular, quantum interference involving both RS and FSS has not been demonstrated experimentally. Here, through detection of time-resolved resonance fluorescence from a QD neutral exciton driven in the Rabi regime (Fig. 1), we experimentally demonstrate triple-slit-type quantum interference in a V-type three-level artificial atom [3]. This result is of fundamental interest in the experimental studies of the properties of V-type systems and may pave the way for further insight into their coherence properties. It also suggests QDs as candidates for multi-path-interference experiments for probing foundational concepts in quantum physics [4]. [1] Haroche, S. & Raimond, J.-M. Exploring the Quantum: Atoms, Cavities, and Photons. OUP Oxford, (2006). [2] Dada, A. C., et al. Optica 3, 493–498 (2016). [3] Dada, A. C., et al. arXiv preprint arXiv:1703.02308 (2017). [4] Sinha, U., Couteau, C., Jennewein, T., Laflamme, R., & Weihs, G. Science 329, 418–421 (2010).
When internal states of atoms are manipulated using coherent optical or radio-frequency (rf) radiation, it is essential to know the polarization of the radiation with respect to the quantization axis of the atom. We first present a measurement of the two-dimensional spatial distribution of the electric-field amplitude of a linearly polarized pulsed rf electric field at $\ensuremath{\sim}25.6\phantom{\rule{0.28em}{0ex}}\mathrm{GHz}$ and its angle with respect to a static electric field. The measurements exploit coherent population transfer between the 35s35s35s and 35p35p35p Rydberg states of helium atoms in a pulsed supersonic beam. Based on this experimental result, we develop a general framework in the form of a set of equations relating the five independent polarization parameters of a coherently oscillating field in a fixed laboratory frame to Rabi rates of transitions between a ground and three excited states of an atom with arbitrary quantization axis. We then explain how these equations can be used to fully characterize the polarization in a minimum of five Rabi-rate measurements by rotation of an external bias field, or, knowing the polarization of the driving field, to determine the orientation of the static field using two measurements. The presented technique is not limited to Rydberg atoms and rf fields but can also be applied to characterize optical fields. The technique has the potential for sensing the spatiotemporal properties of electromagnetic fields, e.g., in metrology devices or in hybrid experiments involving atoms close to surfaces.
Transient nonlinear optical spectroscopy, performed on excitons confined to single GaAs quantum dots, shows oscillations that are analogous to Rabi oscillations in two-level atomic systems. This demonstration corresponds to a one-qubit rotation in a single quantum dot which is important for proposals using quantum dot excitons for quantum computing. The dipole moment inferred from the data is consistent with that directly obtained from linear absorption studies. The measurement extends the artificial atom model of quantum dot excitonic transitions into the strong-field limit, and makes possible full coherent optical control of the quantum state of single excitons using optical pi pulses.
We analyze theoretically the quantum beat and the polarization interference phenomena observed as oscillations in pulsed four-wave mixing. We show that resolution of the signal with respect to the delay between the incoming pulses as well as the detection frequency provides valuable information on the nature of the oscillations. Most importantly, it is very simple to distinguish between polarization interference from two independent optical transitions and quantum beats from a three-level system. In case of polarization interference, the phase of the oscillations shifts \ensuremath{\pi} when the detected frequency passes any of the resonances. In case of quantum beat, the phase has little dependence on the detected frequency near the resonance.