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Modelling of quantum memories based on atomic external degrees of freedom

Juan Carlos CHAVES CAPELLA

Published Jun 30, 2023• 0 citations
OpenAlex

Abstract

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.

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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.
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 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 modeling the atom as a wave packet in momentum space with a given initial uncertainty. We 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: (1) the Recoil entanglement regime (which arises in the small momentum uncertainty region) where recoil effects dominate the mechanisms that originate entanglement, and (2) 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. Physical considerations are made to explain the nature of each entanglement regime as well as provide their respective thresholds.
We present an experimental study of two optical quantum memory systems based on electromagnetically induced transparency (EIT) in cold cesium atoms.We explain the relevance of quantum memories for the development of large-scale quantum networks, we give a comprehensive theory of the EIT phenomenon and underline the role of relevant parameters regarding the implementation of quantum memories.The first system under study is prepared in a free-space magneto-optical trap. The main result of this thesis is the demonstration of the spatial multimode capability of this system at the quantum level. For this, we used Laguerre-Gaussian (LG) light beams, i.e. beams possessing a non-zero value of orbital angular momentum (OAM). In a first step, we showed that the orbital angular momentum of stored light pulses is preserved by the memory, deep in the single photon regime. In a second step, we encoded information in the orbital angular momentum state of a weak light pulse and defined a qubit using two LG beams of opposite helicities. We developed an original setup for the measurement of this OAM qubit and used it to characterize the action of the memory during the storage of such a light pulse. Our results show that the memory performs the quantum storage of such a qubit.The second system under study, also a cloud of cold atoms, has the specificity that the atoms are trapped optically in the vicinity of a nano-waveguide. This innovative design ensures a higher light-matter interaction and facilitates the interfacing of photons into and out of the memory. We describe the building of this setup and the first steps towards quantum memory implementations.
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.
Correlated light generated from atomic ensembles can have a central role in prominent quantum information protocols, such as long-distance quantum communication. Here we present our studies on three topics involving the generation of correlated light with four-wave mixing (FWM) in a cold atomic ensemble for applications in quantum communications with high capacity. We experimentally investigate the generation of light with seeded FWM in cold cesium atoms and the time correlations of photon pairs generated with spontaneous FWM. We theoretically investigate the correlations in orbital angular momentum of photon pairs generated with spontaneous FWM for a range of experimental geometries. These studies represent foundational work toward the control and measurement of high-dimensional entanglement in the orbital angular momentum degree of freedom photon pairs for use in high-dimensional quantum communication.
Abstract Electromagnetic waves have both spin momentum and orbital angular momentum (OAM). Light carrying OAM has broad applications in micro-particle manipulation, high-precision optical metrology, and potential high-capacity optical communications. In the concept of quantum information, a photon encoded with information in its OAM degree of freedom enables quantum networks to carry much more information and increase their channel capacity greatly compared with those of current technology because of the inherent infinite dimensions for OAM. Quantum memories are indispensable to construct quantum networks. Storing OAM states has attracted considerable attention recently, and many important advances in this direction have been achieved during the past few years. Here we review recent experimental realizations of quantum memories using OAM states, including OAM qubits and qutrits at true single photon level, OAM states entangled in a two-dimensional or a high-dimensional space, hyperentanglement and hybrid entanglement consisting of OAM and other degree of freedom in a physical system. We believe that all achievements described here are very helpful to study quantum information encoded in a high-dimensional space.