We report on magnetic-field induced transparency (MIT) based on Ramsey electromagnetically induced absorption (EIA) in a paraffin-coated Rb vapor cell. Changing the laser polarization from linear to circular in the presence of a weak residual transverse magnetic field to the laser propagation, the narrow absorption due to the Ramsey EIA transformed into the transparency due to MIT of the 5S1/2 (F = 2)–5P3/2 (F′ = 3) transition of 87Rb in the paraffin-coated Rb vapor cell. The spectral widths of the EIA and MIT in the Hanle configuration were measured to be 0.6 mG (425 Hz) and 1.2 mG, respectively. MIT depended on the long preservation time of the ground-state coherent spin states and the transverse magnetic field. From the numerical results, the crossover between the Ramsey EIA and the MIT could be illustrated as the superposition of both signals.
© 2014 Optical Society of America
Atomic coherence, generated by the interaction of multi-level atoms and light, is of interest for applications in various fields of atomic physics such as atomic spectroscopy, precision measurement, and quantum optics [1–10]. Important well-known atomic coherence phenomena caused by the quantum interference of atomic states include electromagnetically induced transparency (EIT), electromagnetically induced absorption (EIA), and coherent population trapping (CPT) [1–3]. Recently, quantum coherent processes have been intensively studied in artificial atomic systems such as superconducting circuits , quantum dots , metamaterials , optomechanics , and nitrogen-vacancy centers in diamond .
Comparing the EIA due to spontaneous coherence transfer with the EIT due to two-photon coherence, the generation mechanism of atomic coherence for EIA is completely different from that for EIT, due to the destructive quantum interference on the two-photon resonance with two optical fields. In EIA, atomic coherence between degenerate excited levels is transferred spontaneously to degenerate ground levels; a process known as spontaneously transferred atomic coherence (STAC) [16–25]. Although a narrow spectral width is an important characteristic of the atomic coherence phenomena, it is difficult to observe the EIA effect in atomic vapor cells with buffer gases which is typically used for narrow EIT spectrum [16–23]. This is so because the EIA is sensitive to the decay rates of the excited states, which is determined by the atomic collisions in the buffer gas or with the cell walls. Almost all studies of EIA have been limited by wall collisions and transit-time broadening in pure atomic vapor cells. Recently, Ramsey EIA with a narrow sub-kHz spectral width has been reported using a paraffin-coated Rb vapor .
However, the atomic transitions between Zeeman sublevels have different routes according to the laser polarization, and the atomic-magnetic-momentum changes according to the static magnetic fields. The effects of the static magnetic field and the polarization of the incident laser on the EIT, CPT, and EIA resonances have been reported for pure vapor cells [26–30]. Recently, it was reported that the CPT of the Hanle configuration could be transformed into a narrow absorption signal in both the vapor cell with buffer gas and the paraffin-coated call in a weak transverse magnetic field, when the laser polarization was changed from linear to circular [31, 32]. This narrow absorption in the Hanle configuration, induced by the transverse magnetic field in the CPT medium, was termed magnetic-field-induced absorption (MIA) , and we speculated on whether it was possible to also observe magnetic-field-induced transparency (MIT), which is the counterpart phenomenon of MIA. To the best of our knowledge, MIT has not been observed under conditions of narrow Ramsey EIA in an anti-relaxation-coated vapor cell.
Here, we report the observation of the MIT phenomenon of the 5S1/2 (F = 2) → 5P3/2 (F′ = 3) transition of 87Rb in a paraffin-coated Rb vapor cell under conditions of EIA due to the wall-induced Ramsey effect. We investigated the crossover between the narrow Ramsey EIA and MIT spectra as a function of the laser polarization varying from linear to circular, and the features of the transformation of EIA into MIT in a paraffin-coated cell are compared with those in a pure cell. The Ramsey EIA and MIT spectra in an anti-relaxation-coated cell were investigated theoretically for an eight-level closed W-type atomic system by considering multiple atomic interactions through the laser beam in the presence of a weak residual magnetic field.
2. Experimental setup
The effective EIA has been found under conditions of a closed atomic system of the Fg → Fe = Fg + 1 transition [16–19]. Our experiment for EIA was achieved with the 5S1/2 (F = 2) → 5P3/2 (F′ = 3) cycling transition of 87Rb, which is a closed atomic system without population leakage, as shown in Fig. 1. Considering a transverse magnetic field (Bt) in the Hanle configuration with scanning of the longitudinal magnetic field (Bl), we deal with all transitions between the magnetic sublevels: σ+ (Δm = + 1), σ– (Δm = −1), and π (Δm = 0) transitions. When Bl is used as the quantization axis, the linearly polarized laser induces the σ+ (Δm = + 1) and σ– (Δm = −1) transitions between the magnetic sublevels because the linearly polarized light may be considered as being composed of counter-rotating circularly polarized components. As shown in Fig. 1, the W-type configuration is generated between the Zeeman sublevels of the 5S1/2 (F = 2) → 5P3/2 (F′ = 3) transition by the σ+ and σ– transitions. However, if the quantization axis is taken to be in the direction of the external magnetic field in the presence of a transverse magnetic-field component, then a circularly polarized laser can induce the π (Δm = 0) and σ ± (Δm = ± 1) transitions between the magnetic sublevels .
Figure 2 shows our experimental setup for investigating Ramsey EIA and MIT in the Hanle configuration. The laser system is an external cavity diode laser (ECDL) stabilized to the 5S1/2 (F = 2) → 5P3/2 (F′ = 3) transition. The laser polarization was controlled using a half-wave plate (HWP) and a quarter-wave plate (QWP). The laser beam size was fixed by using an aperture with a diameter of 2 mm. A 5-cm-long 2.5-cm-diameter paraffin-coated Rb vapor cell at room temperature was installed in a solenoid coil surrounded by a μ-metal chamber. When the directions of the linearly polarized laser and laser propagation are set to be along the x- and z-axes, respectively, Bt and Bl are parallel to the linearly polarized laser (x-axis) and laser propagation direction (z-axis), respectively. For observation of the EIA and MIT spectra in the Hanle configuration, Bl was slowly scanned over a range of ± 20 mG. The laser power was measured passing through the paraffin-coated Rb vapor cell with a photo-detector (PD).
3. Experimental results and discussion
When Bl was slowly scanned over the range −175 mG to + 175 mG, we observed the double-structure EIA spectrum in the paraffin-coated vapor cell of the 5S1/2 (F = 2) → 5P3/2 (F′ = 3) transition of 87Rb atoms, as shown in Fig. 3, where the laser intensity was estimated to be 3.0 μW/mm2. The very narrow EIA seen in Fig. 3 is a result of the EIA Ramsey interference of the preserved atomic coherence with the atoms returning to the laser beam after multiple collisions with the paraffin-coated wall. The absorption of all figures in our manuscript is described as linear scale. In particular, the mechanism of EIA Ramsey interference is understood as interference between the first and second STACs maintained after multiple wall collisions with the paraffin-coated wall. As the number of collisions with the wall for which the atomic coherence is retained increases, the atomic coherence lifetime increases, and the spectral width of the Ramsey EIA spectrum is inversely proportional to the atomic coherence lifetime . The Ramsey EIA resonance width was measured to be 0.6 mG, corresponding to 425 Hz, and is related to the time that the atomic coherence among the Zeeman sublevels of the 5S1/2(F = 2) state is maintained after several wall collisions. The broad EIA resonance around the narrow Ramsey EIA peak arises from STAC of the single interaction of atoms with the laser. The spectral width of this broad EIA resonance is determined by the interaction transit time. The general EIA spectrum has been observed previously in a pure atomic vapor cell [16–23].
We investigated the laser polarization effects of the Ramsey EIA medium in the presence of the weak transverse magnetic field, as shown in Fig. 4(a). The QWP angle indicated in the figure is that between the linear polarization direction and the fast axis of the QWP. When the polarization of the laser was changed from linear to circular by the QWP, we found that the narrow absorption resonance due to the Ramsey EIA effect gradually transformed into transparency resonance. To the best of our knowledge, this is the first observation of the narrow MIT phenomenon in a paraffin-coated cell.
In the case of atoms interacting with circularly polarized light, if Bl is used as the quantization axis, almost all the population is focused on the transition between the two magnetic sublevels mF = ± 2 of 5S1/2 (F = 2) and mF′ = ± 3 of 5P3/2 (F′ = 3) because of the optical pumping effect. The relative transition probability of this transition is higher than that of the other transitions, and the relative absorption in the circular polarization configuration is higher than that in the case of linear polarization. We can see in Fig. 4(a) that the background absorption increases with the circular polarization. In this configuration and with the quantization axis parallel to the laser propagation direction, there are no atomic coherence effects due to STAC or two-photon resonance. Intuitively, a signal with a sub-natural width would not be expected in the circular polarization configuration.
However, if there is a weak Bt, then the atomic magnetic momentum can be changed by changing the direction of the external magnetic field because the external magnetic-field direction dominates the weak Bt around Bl = 0. When the direction of Bt is used as the quantization axis, the circularly polarized laser induces π- and σ ± -transitions between the magnetic sublevels. Near Bl = 0, we can observe the narrow transparency phenomenon due to the external-magnetic-field-induced atomic magnetic momentum in the presence of a weak Bt, and the π- and σ ± -transitions contribute to TOC and two-photon atomic coherence effects, which are unexpected in the σ+ or σ– transition configurations. Therefore, the main cause of the spectral narrowing of the MIT resonance is the long atomic coherence in the anti-relaxation-coated cell. The MIT resonance width was measured to be 1.1 mG and is limited by the Ramsey EIA resonance width.
To confirm the atomic coherence effect in MIT, we investigated EIA and MIT in the pure Rb vapor cell in the presence of a weak transverse magnetic field. Figure 4(b) shows the transmittance spectrum in the pure Rb vapor cell as a function of the laser polarization under the same conditions as those for Fig. 4(a). Here, the spectral width of the EIA resonance for an incident linear polarization was measured to be approximately 150 mG. From the EIA resonance widths in the paraffin-coated cell and the pure cell, we estimated the atomic coherence time in the pure cell to be more than 200 times shorter than that in the paraffin-coated cell. When the laser polarization was changed to be circular, the magnitude of the EIA resonance decreased to zero without any MIT effect, as shown in Fig. 4(b). The MIT effect was not observed in the pure Rb cell because of the short atomic coherence. Therefore, the narrow MIT in the paraffin-coated cell can be understood as sensitive detection of the external-magnetic-field-induced atomic magnetic momentum change in the EIA medium with a long atomic coherence.
To investigate theoretically the transformation of Ramsey EIA into MIT in an anti-relaxation-coated vapor cell, we numerically calculated an eight-level atomic system based on the F = 1 → F′ = 2 transition that includes degenerate magnetic sublevels, with the STAC term between degenerate excited levels transferring spontaneously to degenerate ground levels. The time-dependent Schrödinger equation can be expressed as:28]. Furthermore, repeated interactions between the atoms and walls in the anti-relaxation-coated vapor cell were considered, and it should be noted that changing the quantization axis to be along one direction of the external magnetic field (Bl or Bt) affects the effective transitions among the degenerate magnetic sublevels.
Figure 5(a) presents the numerical simulation results showing the transformation of the Ramsey EIA interference fringes for an incident linear polarization (QWP = 0°) into the MIT for an incident circular polarization (QWP = 45°) at a Rb atom velocity of 280 m/s, where the values on the right represent the angle between the linear polarization direction and the fast axis of the QWP. The numerical calculations were performed for a laser intensity of 3.0 μW/mm2, laser beam diameter of 2 mm, and a transverse magnetic field of 150 μG. The Ramsey EIA interference fringes are described approximately by a cosine wave with absorption phase at Bl = 0. When the QWP angle was changed from 0° to 45°, the amplitude of the Ramsey EIA interference decreased but that of the MIT signal increased. The spectrum of the elliptical polarization can be described as the superposition of both the Ramsey EIA interference and MIT signal. The MIT signal is completely different from the Ramsey EIA fringes because the cause of MIT is the magnetic-field-induced effective transitions. Although the MIT is not due to quantum interference effects, the spectral width of the Ramsey EIA affects the width and magnitude of the MIT spectrum. This means that the preservation time of the ground-state coherent spin states is strongly related to the width and magnitude of the MIT spectrum.
Since the evolution of the ground-state atomic coherence is evaluated for a given atomic velocity, the period and amplitude of the Ramsey EIA fringes depend on the atomic velocity. To compare the calculated results with the experiment results of Fig. 4(a), we considered a Maxwell–Boltzmann distribution of the atomic velocities. Figure 5(b) shows the numerical simulation results for the transformation of the Ramsey EIA into MIT according to the QWP angle using parameters equal to the experimental conditions of Fig. 4(a). The spectral shape in the anti-relaxation-coated vapor cell is obtained by integrating over all the interaction times according to the velocities of the atoms. In the case of the linearly polarized laser (QWP = 0°), the Ramsey EIA resonance appeared because of the superposition of many Ramsey interference fringes for different atomic velocities. When the laser polarization was changed to be circular (QWP = 45°), the Ramsey EIA resonance transformed into the MIT signal. The calculated results in Fig. 5(b) are in good agreement with the experimental results of Fig. 4(a) for the paraffin-coated vapor cell. Also, our results are related to coherent population oscillations and ground-state coherence [33, 34]. We plan to investigate coherent population oscillations in the anti-relaxation-coated vapor cell.
We have investigated the transformation of Ramsey EIA into MIT in a paraffin-coated Rb vapor cell in the presence of a weak transverse magnetic field. The narrow Ramsey EIA resonance of the 5S1/2 (F = 2)-5P3/2 (F′ = 3) transition of 87Rb resulted from maintaining the STAC between degenerate magnetic sublevels, even after multiple wall collisions with the paraffin-coated wall. When the laser polarization was changed from linear to circular in the presence of a weak residual transverse magnetic field to the laser propagation direction, the Ramsey EIA transformed into transparency because the transition paths change according to the value of the longitudinal magnetic-field strength. In particular, the long lifetime of the STAC in the paraffin-coated EIA medium is significantly related to the width and magnitude of the MIT. In our experiment, the spectral widths of the Ramsey EIA and MIT resonances were measured to be 0.6 mG and 1.1 mG, respectively. The MIT in the paraffin-coated cell has a long atomic coherence time, whereas that in the pure cell has a short atomic coherence time, meaning that the MIT effect could not be observed in the pure Rb cell. The sensitivity of the MIT depends on the transverse magnetic-field amplitude and the atomic coherence time of the EIA medium. In particular, the transverse magnetic-field is important factor for the MIT effect. To understand the transformation of EIA into MIT in the paraffin-coated vapor cell, we numerically calculated the density matrix equations for the eight-degenerate magnetic sublevels based on the F = 1 → F′ = 2 transition. The calculated Ramsey EIA interference fringes for incident linear polarization transformed into MIT for incident circular polarization at an atomic velocity of 280 m/s, and the calculated spectra were described as a superposition of both the Ramsey EIA interference and MIT signal according to the laser polarization. From the calculated results, we were able to illustrate the crossover from the Ramsey EIA interference fringes to the MIT signal. The dynamics between the Ramsey EIA and MIT spectra according to the laser polarization were simulated considering a Maxwell–Boltzmann atomic velocity distribution, and the numerical results were shown to be in good agreement with the observed spectra. Although the origin of MIT is not two-photon quantum interference, the crossover from Ramsey EIA to MIT resonance in an anti-relaxation-coated vapor cell could be used as a vector magnetometer to distinguish longitudinal and transverse magnetic-field amplitudes.
We thank Heung-Ryoul Noh for valuable discussion. This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (Grant#2012R1A2A1A01006579).
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