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Experimental and Theoretical Study of Two Non-linear Processes Induced by Ultra-narrow Resonances in Atoms

Chitram Banerjee

Published Jun 17, 2019• 0 citations
Publisher

Abstract

In this PhD work, two distinct phenomena are considered, which are both related to non-linear interactions between light and atoms. The first part of the thesis is dedicated to four wave mixing based on the internal degrees of freedom of room temperature helium atoms and uses it for amplification processes and generation of squeezed light. The second studied process is based on external degrees of freedom of cold cesium atoms and used for light storage and phase conjugate field generation through multi-wave mixing. I experimentally observed and characterized phase sensitive amplification via four-wave mixing in metastable helium at room temperature. I have obtained about 9 dB of maximum gain with a bandwidth of about 300 kHz. The obtained phase transfer functions showed a strong phase squeezing, indicating that the phenomenon was almost free of unwanted processes. In the second part, I explain how recoil induced resonances, which are due to the transfer of momentum between a photon and an atom, can be used to store light. I also explain how this phenomenon can lead to generation of a phase conjugate field, and why the existing theory fails to model the dip, which appears in the phase conjugate generation spectrum when the field power is increased. I extend the model to the fifth order so that it can reproduce this new feature and demonstrate that it depends on the decay rate of the coherence, which is excited between atomic levels of different momenta. I then show that a simpler model, which is based on three levels defined by internal and external degrees of freedom of the atom, can explain the observed phenomenon.

DOI
10.70675/aebac5b6zb01fz4f5bz9679zcaac1f697e67

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In this PhD work, two distinct phenomena are considered, which are both related to non-linear interactions between light and atoms. The first part of the thesis is dedicated to four wave mixing based on the internal degrees of freedom of room temperature helium atoms and uses it for amplification processes and generation of squeezed light. The second studied process is based on external degrees of freedom of cold cesium atoms and used for light storage and phase conjugate field generation through multi-wave mixing. I experimentally observed and characterized phase sensitive amplification via four-wave mixing in metastable helium at room temperature. I have obtained about 9 dB of maximum gain with a bandwidth of about 300 kHz. The obtained phase transfer functions showed a strong phase squeezing, indicating that the phenomenon was almost free of unwanted processes. In the second part, I explain how recoil induced resonances, which are due to the transfer of momentum between a photon and an atom, can be used to store light. I also explain how this phenomenon can lead to generation of a phase conjugate field, and why the existing theory fails to model the dip, which appears in the phase conjugate generation spectrum when the field power is increased. I extend the model to the fifth order so that it can reproduce this new feature and demonstrate that it depends on the decay rate of the coherence, which is excited between atomic levels of different momenta. I then show that a simpler model, which is based on three levels defined by internal and external degrees of freedom of the atom, can explain the observed phenomenon.
This thesis describes the theoretical solution and experimental verification of phase conjugation via nondegenerate four-wave mixing in resonant media. The theoretical work models the resonant medium as a two-level atomic system with the lower state of the system being the ground state of the atom. Working initially with an ensemble of stationary atoms, the density matrix equations are solved by third-order perturbation theory in the presence of the four applied electro-magnetic fields which are assumed to be nearly resonant with the atomic transition. Two of the applied fields are assumed to be non-depleted counterpropagating pump waves while the third wave is an incident signal wave. The fourth wave is the phase conjugate wave which is generated by the interaction of the three previous waves with the nonlinear medium. The solution of the density matrix equations gives the local polarization of the atom. The polarization is used in Maxwell's equations as a source term to solve for the propagation and generation of the signal wave and phase conjugate wave through the nonlinear medium. Studying the dependence of the phase conjugate signal on the various parameters such as frequency, we show how an ultrahigh-Q isotropically sensitive optical filter can be constructed using the phase conjugation process. In many cases the pump waves may saturate the resonant medium so we also present another solution to the density matrix equations which is correct to all orders in the amplitude of the pump waves since the third-order solution is correct only to first-order in each of the field amplitudes. In the saturated regime, we predict several new phenomena associated with degenerate four-wave mixing and also describe the ac Stark effect and how it modifies the frequency response of the filtering process. We also show how a narrow bandwidth optical filter with an efficiency greater than unity can be constructed. In many atomic systems the atoms are moving at significant velocities such that the Doppler linewidth of the system is larger than the homogeneous linewidth. The latter linewidth dominates the response of the ensemble of stationary atoms. To better understand this case the density matrix equations are solved to third-order by perturbation theory for an atom of velocity v. The solution for the polarization is then integrated over the velocity distribution of the macroscopic system which is assumed to be a gaussian distribution of velocities since that is an excellent model of many real systems. Using the Doppler broadened system, we explain how a tunable optical filter can be constructed whose bandwidth is limited by the homogeneous linewidth of the atom while the tuning range of the filter extends over the entire Doppler profile. Since it is a resonant system, sodium vapor is used as the nonlinear medium in our experiments. The relevant properties of sodium are discussed in great detail. In particular, the wavefunctions of the 3S and 3P states are analyzed and a discussion of how the 3S-3P transition models a two-level system is given. Using sodium as the nonlinear medium we demonstrate an ultrahigh-Q optical filter using phase conjugation via nondegenerate four-wave mixing as the filtering process. The filter has a FWHM bandwidth of 41 MHz and a maximum efficiency of 4 x 10-3. However, our theoretical work and other experimental work with sodium suggest that an efficient filter with both gain and a narrower bandwidth should be quite feasible.
Recoil-induced resonances (RIR) can be detected in experiments involving light-atom interaction where atomic external degrees of freedom play an important role. In pump-probe experiments the recoil of atoms due to absorption and emission of radiation is responsible for the amplification and attenuation of the probe beam under certain circumstances, resulting in a disperse and narrow (of the order of 10 kHz) feature in the spectrum of the probe beam. Backward four-wave mixing (BFWM) signals, via recoil-induced resonances, using cold atoms as nonlinear medium were also extensively studied during the past years. In this work it will be presented a systematic study of forward four-wave mixing (FFWM) via RIR. It will be also presented a simple theoretical model that allowed us to predict the lineshapes of the observed signals and to better understand the phenomenon studied. The model is also compared with results that are already known in order to verify its validity and predict the possibility of measure the velocity distribution of the atomic cloud in a future experiment.
In this work, we perform a detailed theoretical and experimental investigation of an atomic memory based on recoil-induced resonance in cold cesium atoms. We consider the interaction of nearly degenerate pump and probe beams with an ensemble of two-level atoms. A full theoretical density matrix calculation in the extended Hilbert space of the internal and external atomic degrees of freedom allows us to obtain, from first principles, the transient and stationary responses determining the probe transmission and the forward four-wave-mixing spectra. These two signals are generated together at the same order of perturbation with respect to the intensities of pump and probe beams. Moreover, we have investigated the storage of optical information on the spatial modes of light beams in the atomic external degrees of freedom, which provided a simple interpretation for the previously reported nonvolatile character of this memory. The retrieved signals after storage reveal the equivalent role of probe transmission and four-wave mixing, as the two signals have similar amplitudes. Probe transmission and forward four-wave-mixing spectra were then experimentally measured for both continuous excitation and after storage. The experimental observations are in good agreement with the developed theory, and they open another pathway for the reversible exchange of optical information with atomic systems.
In this work, we present some fundamental tools in the modelling of quantum networks. We intend to develop theoretical tools such as the usage of the mixed variables density matrix formalism to model from first principles atomic experiments where external degrees of free- dom play an important role, and entanglement quantification in atom-photon systems where entanglement is present in the continuous variables of the system. Namely, we first perform a detailed theoretical and experimental investigation of an atomic memory based on recoil- induced resonance in cold cesium atoms. We consider the interaction of a nearly degenerated pump and probe beams with an ensemble of two-level atoms. A full theoretical density ma- trix calculation in the extended Hilbert space of the internal and external atomic degrees of freedom allows us to obtain, from first principles, the transient and stationary responses de- termining the probe transmission and the forward four-wave mixing spectra. These two signals are generated together at the same order of perturbation with respect to the intensities of pump and probe beams. Moreover, we have investigated the storage of optical information on the spatial modes of light beams in the atomic external degrees of freedom, which provided a simple interpretation for the previously-reported non-volatile character of this memory. The retrieved signals after storage reveal the equivalent role of probe transmission and four-wave mixing, as the two signals have similar amplitudes. Probe transmission and forward four-wave- mixing spectra were then experimentally measured for both continuous excitation and after storage. The experimental observations are in good agreement with the developed theory and open a new pathway for the reversible exchange of optical information with atomic systems. Next, we review the Weisskopf-Wigner formalism for spontaneous emission considering the spatial modes of light as well as external atomic degrees of freedom which we introduce in the theory by modelling the atom as a wavepacket in momentum space with a given initial uncertainty, and perform a purity calculation in order to quantify the entanglement encoded in the momentum variables of the atom-photon system. Our purity calculations reveal two high entanglement regimes depending on the initial atomic momentum uncertainty: the Recoil entanglement regime (which arises in the small momentum uncertainty region), where recoil effects dominate the mechanisms that originate entanglement and the Doppler entanglement regime (in the large momentum uncertainty region) where homogeneous Doppler shifts in the emitted photon’s frequency play the fundamental part in the build up of quantum correlations in the system. Simplified expressions for the system’s wavefunction are found for each of the entanglement regimes and physical considerations are made to explain their nature. Finally, we briefly investigate the role of entanglement in the distinguishability of two physically different quantum states that arise naturally from the theory, where we note that entanglement in the system leads to a better resolution of the two quantum states.
We demonstrate the possibility to generate squeezed vacuum states of light by four wave mixing (FWM) enabled coherent population trapping in a metastable helium cell at room temperature. Contrary to usual FWM far detuned schemes, we work at resonance with an atomic transition. We investigate the properties of such states and show that the noise variances of the squeezed and anti-squeezed quadratures cannot be explained by the simple presence of losses. A specific model allows us to demonstrate the role played by spontaneous emitted photons, which experience squeezing while propagation inside of the cell. This theoretical model, which takes into account both residual absorption and spontaneous emission, leads to an excellent agreement with the experimental data without any adjusted parameter.
Quantum interference in atomic media has elicited interest for a very wide range of investigations and applications. As well as being a fascinating effect in itself, it also found applications in spectroscopy, nonlinear optics and has recently been drawing attention in the field of quantum optics for the realisation of sources of entangled photons, optical switching, and quantum information storage. The work presented in this thesis consists of two main projects centred around the theme of quantum interference in atomic processes. As cooled atomic vapours provide favourable conditions for the investigation of coherent phenomena, a magneto-optical trap was built for the future study of quantum interference in four-level link- ages. The number of trapped atoms is estimated to be ≈ 8 × 10^8, and the density to be ≈ 10^9 atoms per cubic centimetre. This represents the first stage of an ongoing study of quantum interference in four-level linkages. However, coherent effects can also be observed in hot vapours. A spontaneous, highly efficient, frequency up-conversion arising from four-wave mixing can indeed be observed in Rubidium. This complex phenomenon was investigated experimentally and theoretically so as to improve the conversion efficiency, and understand the underlying physics. The optimum conditions found in this study yield 1 mW of converted light for 40 mW of pumping light. As part of the study of the phase coherence of the process, the conversion of spatial modes in the four-wave mixing process was also examined. The observation of the transfer of orbital angular momentum in the process is reported, and a preliminary theoretical interpretation is presented.