Bose-Einstein condensates of ultracold atoms serve as low-entropy sources for a multitude of quantum-science applications, ranging from quantum simulation and quantum many-body physics to proof-of-principle experiments in quantum metrology and quantum computing. For stability reasons, in the majority of cases the energetically lowest-lying atomic spin state is used. Here, we report the Bose-Einstein condensation of caesium atoms in the Zeeman-excited mf = 2 state, realizing a non-ground-state Bose-Einstein condensate with tunable interactions and tunable loss. We identify two regions of magnetic field in which the two-body relaxation rate is low enough that condensation is possible. We characterize the phase transition and quantify the loss processes, finding unusually high three-body losses in one of the two regions. Our results open up new possibilities for the mixing of quantum-degenerate gases, for polaron and impurity physics, and in particular for the study of impurity transport in strongly correlated one-dimensional quantum wires.

The effect of a vector magnetic field was studied on electromagnetically induced transparency (EIT) with linear ⊥ linear polarization of the probe and pump beams in 87Rb−D2 transition with a vapor cell at room temperature. The dependence of EIT on the direction of the quantization axis and the relative orientation of the polarizations of the applied electric fields was studied experimentally. We show that from the relative strengths of σ and π EITs, the direction of the magnetic field can be found. Moreover, from the relative separation between σ and π EITs, the strength of the magnetic field can be calculated. We also demonstrate that the EIT peak amplitudes show oscillatory behavior depending upon the orientation of the laser polarization relative to the magnetic field direction. To understand the experimental observations, a theoretical study was done numerically considering all 13 Zeeman sub-levels. Apart from the numerical simulation, a toy model was also constructed to obtain an analytical response of the medium considering the velocity distribution. The dependencies of the magnetic field direction and polarization direction of the electric field were explicitly derived with the analytical model.

The dependencies of the polarization rotation on the probe ellipticity and the longitudinal magnetic field have been studied both experimentally and theoretically in a V-type electromagnetically induced transparency for 87Rb vapour. The angle of rotation varies periodically with the change in the probe ellipticity and non-linearly with the variation of the magnetic field. We have observed that the plane of polarization is rotated maximum for linearly polarized light and have obtained angle of rotation 0.32°±0.01° for B=0.036±0.001 mT while it was 0.0267°±0.0002° without magnetic field. Thus our measurement becomes sensitive to the low magnetic field. A four-level system is considered and the corresponding density matrix equations have been solved analytically to explain these observations theoretically with the help of degenerate and non-degenerate magnetic sub-levels.

The dependency of polarization rotation with electromagnetically induced transparency (PREIT) in 87Rb vapor on the angular mismatch between the probe and the pump beams has been studied experimentally and theoretically for a V-type configuration. We have observed a nonlinear variation of the PREIT angle with the angular mismatch. The angular mismatch enhanced the residual Doppler broadening effect, as well as diminishes the two photon coherence contribution, in the medium. We have also systematically studied the effect of optical depth (OD) and the pump beam spot size variations to understand how the number of interacting atoms affect the two photon coherence contribution of the polarization rotation. The value of group velocity of the probe beam has been calculated from the experimentally observed spectrum. We have modeled a three-level V-type system to explain the experimentally observed phenomena by considering the effect of OD and spot size with angular mismatch in the medium. We have considered two-dimensional Maxwell–Boltzmann distribution to calculate the susceptibilities for all atoms of all velocity components. The characteristic variation of the angle of PREIT with the angular mismatch matches well with the experimentally observed result.

In this article, we have shown that atomic states can be engineered by tuning the coupling Rabi frequency for a system with N-type configuration. Electromagnetically induced transparency (EIT), electromagnetically induced absorption (EIA) and Autler-Townes (AT) splitting have been observed experimentally in a four level N-type atomic vapor of 85Rb atoms in the hyperfine levels of D2 transition. It has been shown that the response of the atomic medium can be tuned from highly transparent to highly absorptive in our case. The evolution of the atomic states from the dark state |D⟩ to the non-coupled state |NC⟩ has been studied with the partial dressed state approach, which makes the backbone of the modification of the atomic response. In addition, the transient solutions in the time domain and the steady state solution in the frequency domain have been studied. The population dynamics and the coherence contribution in each case have been analyzed by time dependent solutions. The experimentally observed steady line-shape profiles have been supported by the steady state solution of optical-Bloch equations considering the Maxwell-Boltzmann velocity distributions of the atoms. It has been observed that the crossover between the EIT and the AT splitting has been replaced by the interference contribution of the EIA in this N-type system.

Pulse delay with the group velocity dispersion (GVD) characteristics was studied in the V-type electromagnetically induced transparency in the hyperfine levels of atoms with a closed system configuration. The phase coherency between the pump and the probe laser beams was maintained. We studied the pulse delay and the GVD characteristics with the variation of the pump Rabi frequency taking optical density (OD) as a parameter. We observed a maximum of 268 ns pulse delay for 21.24 MHz pump Rabi frequency at OD 5.04 of the Rb vapor cell. For a better understanding of the experimental results, we have derived an analytical solution for the delay characteristics considering the thermal averaging. The analytical solution was derived for a three level V-type system. The theoretical plots of the delay and the GVD show the same characteristics as we observed in the experiment. This analytical approach can be further generalized for the higher level schemes to calculate different quantities such as susceptibility, group velocity delay or GVD characteristics.

The dispersive properties of 87Rb atomic medium in electromagnetically induced transparency (EIT) have been studied experimentally as well as theoretically. To measure the dispersion signal, a balanced homodyne detection technique was used by forming a Mach–Zehnder interferometer. We studied the system in a Λ-type configuration. From the slope of the dispersive EIT signal, the group index (ng) of the atomic medium, the group velocity, and the time delay of the light wave through the atomic medium were calculated. We measured the group index of the atomic medium from the dispersion signal and observed that it non-linearly depends on the pump power. This non-linearity signifies that to achieve the maximum reduced group velocity, optimization of the pump power is needed. We got the maximum reduction in the group velocity of the probe beam as m s−1. The corresponding time delay was ns. To support our experimental observation, we have performed a theoretical simulation by taking the semi-classical approach of density matrix formalism of a Λ-type three level system. To get the probe response we solved the optical Bloch equation analytically assuming the Lorentzian velocity distribution of the atom. We have observed that our analytical solution matched exactly with the numerical solution. Our experimental observation of non-linear variation of the group index with the pump Rabi frequency matched quite well with both of our numerical and analytical simulations.

Polarization rotation in electromagnetically induced transparency (PREIT) in rubidium vapour at room temperature has been studied experimentally as well as theoretically in the absence of any magnetic field. PREIT is observed for both 85Rb and 87Rb combining the D1 and the D2 transitions with a V-type configuration. For 85Rb, two EIT peaks and for 87Rb, one EIT peak were observed. Nonlinear characteristics of the variations of the angle of rotation corresponding to the EIT position were observed for both the isotopes of Rb. We have modelled a four level system to explain the occurrence of the double EIT in case of the 85Rb and the occurrence of one EIT peak for 87Rb. The rotation of plane of polarization of the probe beam can be further explained with this model. The characteristic behaviour of the variation of rotation corresponding to the EIT position from theoretical analysis has matched well with the experimental observations. A sharp rotation with a high signal to noise ratio in the vicinity of the EIT can be used as a modulation free and noise insensitive signal for the frequency stabilization.

We report here simultaneous experimental observation of Electromagnetically Induced Transparency (EIT) and Electromagnetically Induced Absorption (EIA) in a multi-level V-type system in D2 transition of Rb87, i.e., F=2→F′ with a strong pump and a weak probe beam. We studied the probe spectrum by locking the probe beam to the transition F=2→F′=2 while the pump is scanned from F=2→F′. EIA is observed for the open transition (F=2→F′=2) whereas EIT is observed in the closed transition (F=2→F′=3). Sub natural line-width is observed for the EIA. To simulate the observed spectra theoretically, Liouville equation for the three-level V-type system is solved analytically with a multi-mode approach for the density matrix elements. We assumed both the pump and the probe beams can couple the excited states. A multi-mode approach for the coherence terms facilitates the study of all the frequency contributions due to the pump and the probe fields. Since the terms contain higher harmonics of the pump and the probe frequencies, we expressed them in Fourier transformed forms. To simulate the probe spectrum, we have solved inhomogeneous difference equations for the coherence terms using the Green’s function technique and continued fraction theory. The experimental line-widths of the EIT and the EIA are compared with our theoretical model. Our system can be useful in optical switching applications as it can be precisely tuned to render the medium opaque and transparent simultaneously.