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arXiv:2103.11729 · Optics Express

Calibration of spin-light coupling by coherently induced Faraday rotation

Rodrigo A. Thomas, Christoffer Østfeldt, Christian Bærentsen, Michal P. Parniak, Eugene S. Polzik

Published Jun 9, 2021• 2 citations
arXivHTMLPDF

Abstract

Calibrating the strength of the light-matter interaction is an important experimental task in quantum information and quantum state engineering protocols. The strength of the off-resonant light-matter interaction in multi-atom spin oscillators can be characterized by the readout rate ΓS. Here we introduce the method named Coherently Induced FAraday Rotation (CIFAR) for determining the readout rate. The method is suited for both continuous and pulsed readout of the spin oscillator, relying only on applying a known polarization modulation to the probe laser beam and detecting a known optical polarization component. Importantly, the method does not require changes to the optical and magnetic fields performing the state preparation and probing. The CIFAR signal is also independent of the probe beam photo-detection quantum efficiency, and allows direct extraction of other parameters of the interaction, such as the tensor coupling ζS, and the damping rate γS. We verify this method in the continuous wave regime, probing a strongly coupled spin oscillator prepared in a warm cesium atomic vapour.

DOI
10.1364/oe.425613

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Calibrating the strength of the light-matter interaction is an important experimental task in quantum information and quantum state engineering protocols. The strength of the off-resonant light-matter interaction in multi-atom spin oscillators can be characterized by the readout rate ΓS. Here we introduce the method named Coherently Induced FAraday Rotation (CIFAR) for determining the readout rate. The method is suited for both continuous and pulsed readout of the spin oscillator, relying only on applying a known polarization modulation to the probe laser beam and detecting a known optical polarization component. Importantly, the method does not require changes to the optical and magnetic fields performing the state preparation and probing. The CIFAR signal is also independent of the probe beam photo-detection quantum efficiency, and allows direct extraction of other parameters of the interaction, such as the tensor coupling ζS, and the damping rate γS. We verify this method in the continuous wave regime, probing a strongly coupled spin oscillator prepared in a warm cesium atomic vapour.
Polarization rotation of weak probe light induced by circularly polarized strong coupling light in a $\ensuremath{\Lambda}$ configuration is studied. We use spin-polarized cold cesium atoms trapped in a magneto-optical trap to remove complications from Zeeman distribution, Doppler broadening, and collisional decoherence. By using a very low probe intensity and short illumination period we work in a strictly linear regime. The probe and the coupling fields are optically phase locked to eliminate phase fluctuation and consequent atomic decoherence. Using this idealized situation we clarify the roles of optically induced Faraday rotation, circular dichroism, and electromagnetically induced transparency (EIT) in determining the final state of the probe light. In particular, we identify an experimental situation where the roles of atomic coherence and EIT are important.
Quantum measurement is one of the most important features of quantum theory. Although mathematical predictions have been verified in great detail, practical implementation has lagged behind. Only recently have people begun to take advantage of quantum measurement properties to produce new technologies. This research helps fill that technological gap by experimental examination of a continuous, optical measurement for an ensemble of cold atomic spins. The essential physics reduces to the interaction between an atomic ensemble and a weak optical field, which has many well known results. While this work demonstrates many novel applications of the interaction, it also shows that the whole can be more than the sum of the individual parts. Starting with basic characterization of the measurement system using laser-cooled cæsium atoms, the mean value of a spin component is obtained in real time. In essence, the angular momentum of the atomic spins creates a Faraday-like rotation in the polarization of a laser probe beam. With slight modifications, additional spin components are also observed, and are shown to be in good agreement with predictions. In measuring spin dynamics, it is important to account for effects of the probe on the spin states as well. Capitalizing on this as a resource, the probe-induced ac-Stark shift is used to transform a quasi-classical spin-coherent state into a highly quantum Schrödinger cat type of superposition between two spin states. Finally, this work combines all the previous results to demonstrate how a continuous measurement of the spin with a carefully crafted evolution created in part by the probe, allows for nearly real-time determination of the complete spin density matrix. In a single 1.5 millisecond run, a spin density matrix is determined with fidelities ranging from about 85% to 90% across a wide spectrum of test states.
Abstract With the help of Stokes operator Ŝ 2 squeezed state (also called polarization squeezed state (PSS)) of 795 nm light, rubidium-87 ( 87 Rb) atomic magnetometer based on Faraday rotation (FR) has been implemented and characterized. The PSS of Stokes operator Ŝ 2 of 795 nm light has been prepared by means of coherently combining the polarization coherent state (PCS) of a linearly p-polarized bright 795 nm light beam and a linearly s-polarized squeezed vacuum state (SVS) generated by a 397.5 nm ultraviolet laser pumped sub-threshold optical parametric oscillator (OPO) with a PPKTP bulk crystal inside the OPO cavity. PSS with a squeezing level of −3.7 ± 0.3 dB has been achieved around the analysis frequency of 10 kHz. At different transitions of D 1 line, various frequency detuning, and reasonable atomic vapor cell’s temperature, FR has been measured and compared. To decrease absorption (scattering) losses and the back-action from atomic spin noise to the probe beam’s polarization noise for maintaining the quantum properties of PSS of Stokes operator Ŝ 2 of 795 nm light, we had to run our magnetometer with 87 Rb vapor cell’s temperature below 60 °C, at which the PSS was almost destroyed. The sensitivities of magnetic field measurement were characterized via measuring signal-to-noise ratio of the alternating current calibrated magnetic field signal with a balanced polarimeter. Under the conditions of the atomic number density of ∼5.8 × 10 10 cm −3 ( T ∼ 40 °C) and the probe beam with a detuning of ∼−400 MHz relative to the 5S 1/2 ( F g = 2) − 5P 1/2 ( F e = 1) transition of 87 Rb D 1 line, a typical sensitivity of ∼19.5 pT (Hz 1/2 ) −1 has been achieved employing PSS of Stokes operator Ŝ 2 as the probe, compared with a sensitivity of ∼28.3pT (Hz 1/2 ) −1 using PCS as the probe. We preliminarily demonstrated that the quantum-enhanced sensitivity in a Faraday-rotation-based 87 Rb atomic magnetometer with the help of PSS of 795 nm light.
Abstract Spin-polarized atomic ensembles probed by light based on the Faraday interaction are a versatile platform for numerous applications in quantum metrology and quantum information processing. Here we consider an ensemble of Alkali atoms that are continuously optically pumped and probed. Due to the collective scattering of photons at large optical depth, the steady state of atoms does not correspond to an uncorrelated tensor-product state, as is usually assumed. We introduce a self-consistent method to approximate the steady state including the pair correlations, taking into account the multilevel structure of atoms. We find and characterize regimes of Raman lasing, akin to the model of a superradiant laser. We determine the spectrum of the collectively scattered photons, which also characterizes the coherence time of the collective spin excitations on top of the stationary correlated mean-field state, as relevant for applications in metrology and quantum information.
We report our study of the magneto-optical effect in a strictly linear regime on spin-polarized cold cesium atoms. Due to the low intensity and the short illumination period of the probe beam, less than 7.5% of the sample atoms change their states by absorbing probe photons. We produce a medium of atoms at rest in either the 6S1∕2,F=3,mF=06{S}_{1∕2},F=3,{m}_{F}=06S1∕2​,F=3,mF​=0 or 6S1∕2,F=3,mF=36{S}_{1∕2},F=3,{m}_{F}=36S1∕2​,F=3,mF​=3 state by optically pumping atoms trapped in a magneto-optical trap. We use the D1D1D1 resonance with large lower and upper state hyperfine splittings as a probe transition to avoid hyperfine mixing from the Zeeman interaction. Under this idealized situation we measure the Stokes parameters in order to find the polarization rotation and circular dichroism experienced by the probe light. We find that there are qualitative differences between the results for the mF=0{m}_{F}=0mF​=0 and mF=3{m}_{F}=3mF​=3 cases. While dispersion and consequent Faraday rotation play a dominant role when the atoms are in the mF=0{m}_{F}=0mF​=0 state, it is dissipation and circular dichroism that are important when they are in the mF=3{m}_{F}=3mF​=3 state. Similarly, while the size of the Faraday rotation and the circular dichroism for the mF=0{m}_{F}=0mF​=0 case scales linearly with the applied magnetic field, for the mF=3{m}_{F}=3mF​=3 case it is the shift of the probe polarization change versus frequency that is linearly proportional to the magnetic field strength.
Spin-exchange relaxation free alkali-metal magnetometers typically operate in the regime of high optical density, presenting challenges for simple and efficient optical pumping and detection. We describe a high-sensitivity Rb magnetometer using a single elliptically polarized off-resonant laser beam. Circular component of the light creates relatively uniform spin polarization while the linear component is used to measure optical rotation generated by the atoms. Modulation of the atomic spin direction with an oscillating magnetic field shifts the detected signal to high frequencies. Using a fiber-coupled distributed feedback laser, we achieve magnetic field sensitivity of 7 fT/Hz7\text{ }\text{fT}/\sqrt{\text{Hz}}7 fT/Hz​ with a miniature $5\ifmmode\times\else\texttimes\fi{}5\ifmmode\times\else\texttimes\fi{}5\text{ }\text{mm}\text{ }\text{Rb}$ vapor cell.