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arXiv:1102.0226 · Journal of Physics B Atomic Molecular and Optical Physics

Microwave dressing of Rydberg dark states

Монсит Танаситтикосол, Jonathan D. Pritchard, Daniel Maxwell, A. Gauguet, Kevin J. Weatherill, R. M. Potvliege, Charles S. Adams

Published Sep 14, 2011• 131 citations
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Abstract

We study electromagnetically induced transparency (EIT) in the 5s$\rightarrow$5p$\rightarrow$46s ladder system of a cold $^{87}$Rb gas. We show that the resonant microwave coupling between the 46s and 45p states leads to an Autler-Townes splitting of the EIT resonance. This splitting can be employed to vary the group index by $\pm 10^5$ allowing independent control of the propagation of dark state polaritons. We also demonstrate that microwave dressing leads to enhanced interaction effects. In particular, we present evidence for a $1/R^3$ energy shift between Rydberg states resonantly coupled by the microwave field and the ensuing breakdown of the pair-wise interaction approximation.

DOI
10.1088/0953-4075/44/18/184020

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arXiv:0807.4251•Physical Review A•Nov 3, 2008•8 citations
We study electromagnetically induced transparency (EIT) in the 5s→\rightarrow→5p→\rightarrow→46s ladder system of a cold 87^{87}87Rb gas. We show that the resonant microwave coupling between the 46s and 45p states leads to an Autler-Townes splitting of the EIT resonance. This splitting can be employed to vary the group index by ±105\pm 10^5±105 allowing independent control of the propagation of dark state polaritons. We also demonstrate that microwave dressing leads to enhanced interaction effects. In particular, we present evidence for a 1/R31/R^31/R3 energy shift between Rydberg states resonantly coupled by the microwave field and the ensuing breakdown of the pair-wise interaction approximation.
We investigate the effect of dressing the dark state in a ladder scheme of electromagnetically induced transparency (EIT) involving a Rydberg state by an optical field. We show that similarly to microwave dressing, the dressing by a laser field induces an Autler–Townes splitting of the EIT resonance which results in an absorption dip while scanning the frequency of the dressing laser. Experimental results show that the full width at half-maximum of the dressing-induced dip can become very narrow as the coupling laser power increases, while the probe transmission change Δ T P exhibits a non-monotonic trend. Numerical simulation using the Lindblad master equation attributes this evolution to a transition from the saturated to the linear regime of absorption. This laser dressing approach enables high-resolution, sub-Doppler measurements in room-temperature environments, providing a precise method for probing hyperfine structures in alkali metal atoms with enhanced clarity. Furthermore, we demonstrate frequency stabilization of a home-made 1064 nm laser to the dressing signal, achieving a stability of 1.5×10 −9 at τ ≈30s.
We initially discuss the theory of three-level systems using the dressed state formalism. One of the dressed states, containing a ground state and a Rydberg state, does not couple with the probe laser; thus, the medium becomes transparent to the latter. This phenomenon is known as electro- magnetically induced transparency (EIT) and this dressed state is known as a Rydberg dark state. We show that EIT can be used to extract the reduced dipole matrix element for transitions to a Rydberg state. However, a prob- lem with three-level Rydberg EIT in a vapour cell is the occurrence of space charges caused by photoelectric ionisation of Rb metal deposited inside the cell. To avoid this problem, we consider adding a third laser resonant with a fourth level. This is to avoid using the laser whose wavelength is less than the threshold wavelength. In cold atoms, the effect of the third laser is to split the usual EIT resonance into a doublet. In thermal atoms, we observe narrow features due to electromagnetically induced absorption and electro- magnetically induced transparency in the Doppler-free configuration. Next we consider the action of a far off-resonance radio frequency (rf) field in the three-level system. We demonstrate the formation of rf-dressed EIT reso- nances in a thermal Rb vapour and show that such states exhibit enhanced sensitivity to dc electric fields compared to their bare counterparts. Fitting the corresponding EIT profile enables precise measurements of the dc field in- dependent of laser frequency fluctuations. We further investigate the theory of rf-dressed Rydberg EIT using the Floquet approach in order to understand the formation of the sideband structure of the Rydberg state. We find that if the time scale of the rf interaction is much shorter than that of the system evolution and decoherence, the sideband structure is well resolved. We also show that the intermediate state exhibits a sideband structure, induced by the Rydberg state, when the Rabi frequency of coupling laser is larger than twice the modulation frequency. Finally we consider resonant microwave cou- pling between the Rydberg states which leads to an Autler-Townes splitting of the EIT resonance in cold atoms. This splitting can be employed to vary the group index by ±10^5 allowing independent control of the absorptive and dispersive properties of the medium, i.e., one can switch the transparency of the medium or control the group velocity of a pulse propagation by tuning on and off the microwave field.
To distinguish the contributions of electromagnetically induced transparency (EIT) and Autler-Townes splitting (ATS) in their applications in precision laser spectroscopy, we propose a real-imaginary spectrum decomposition method to investigate the transparency spectra in a four-level microwave (MW) dressed Rydberg system. We show that the opening transparency windows in the absorption spectra of probe field is a prominent character by EIT, EIT-ATS crossover, and ATS when the MW field is turned off and the intensity of the control field is adjusted. When the MW field is turned on and gradually increased, the EIT is destroyed and disappears. In addition, the most prominent characters that open a transparency window are the EIT-ATS crossover and the ATS. Then, if we further increase the intensity of the MW field, we find that the transparency windows open mainly due to the ATS. Compared to the previous considerations of this issue, which were limited to three-level systems, our four-level scheme reported here is useful for understanding the features of quantum interference in multilevel atomic systems, and has potential applications to study enhanced sensitivity, measurement spectroscopic, quantum processing, quantum communication, and transmission.
Magnetic-field-induced splitting of Rydberg Electromagnetically Induced Transparency (EIT) and Autler-Townes (AT) spectra in 87^{87}87Rb vapor cell
We theoretically and experimentally investigate the Rydberg electromagnetically induced transparency (EIT) and Autler-Townes (AT) splitting of 87^{87}87Rb vapor under the combined influence of a magnetic field and a microwave field. In the presence of static magnetic field, the effect of the microwave field leads to the dressing and splitting of each mFm_FmF​ state, resulting in multiple spectral peaks in the EIT-AT spectrum. A simplified analytical formula was developed to explain the EIT-AT spectrum in a static magnetic field, and the calculations are in excellent agreement with experimental results.We further studied the enhancement of the Rydberg atom microwave electric field sensor performance by making use of the splitting interval between the two maximum absolute mFm_FmF​ states under static magnetic field. The traceable measurement limit of weak electric field by EIT-AT splitting method was extended by an order of magnitude, which is promising for precise microwave electric field measurement.
We propose a general theoretical scheme to investigate the crossover from electromagnetically induced transparency (EIT) to Autler–Townes splitting (ATS) in open ladder-type atomic and molecular systems with Doppler broadening. We show that when the wavenumber ratio kc/kp≈−1, EIT, ATS, and EIT-ATS crossover exist for both ladder-I and ladder-II systems, where kc (kp) is the wavenumber of control (probe) field. Furthermore, when kc/kp is far from −1, EIT can occur, but ATS is destroyed if the upper state of the ladder-I system is a Rydberg state. In addition, ATS exists but EIT is not possible if the control field used to couple the two lower states of the ladder-II system is a microwave field. The theoretical scheme developed here can be applied to atoms, molecules, and other systems (including Na2 molecules, and Rydberg atoms), and the results obtained may have practical applications in optical information processing and transformation.
We offer a general treatment of electromagnetically induced transparency (EIT) in a five level system consisting of four metastable ground states. Two additional rf-microwave fields coherently couple the two ground states of the standard EIT $\ensuremath{\Lambda}$ atom to a pair of additional hyperfine states in the ground state manifold, generating two sets of dressed states that interact via the probe and control lasers, which couple to the electronic excited state. These new hyperfine dressed states manifest themselves in the linear optical susceptibility of the probe as new resonances in addition to the Autler-Townes doublet characteristic of EIT. In particular, we show that the existence of two new narrow resonances, whose width are limited only by ground state decoherence, appear inside the normal EIT transparency window. We show that by controlling the intensity of these rf-microwave fields, one can engineer both the position and width of these narrow resonances and thereby exercise additional control over both the dispersion and group velocity of the probe.