This thesis explores the use of cryogenic rare earth ion doped solids for applications in quantum information science. A theoretical analysis of optically rephased memory protocols, namely the two pulse photon echo, is developed. This analysis is a fully quantum mechanical analysis. The two pulse photon echo suffers from collective amplified spontaneous emission in the output mode due to gain along the direction of propagation. This noise can be 'rephased' with a pi pulse, much like a two pulse photon echo, resulting in time separated nonclassical correlations. This thesis aims to characterize this noise and experimentally realize these nonclassical correlations. A theoretical analysis is presented for a hybrid photon echo rephasing protocol. The protocol uses strong optical rephasing pulses as well as external electric fields to rephase coherence in a two level ensemble of atoms. The Stark effect is utilized to reduce the collective spontaneous emission caused by inversion. We find that the protocol is noise free and has a theoretical maximum efficiency of 54% in the forward direction and 100% in the backward direction. The necessary task of laser frequency stabilization is presented in this thesis. The laser is locked using electronic and optical feedback, named the 'hybrid' lock. A theoretical analysis is presented as well as experimental results. The laser locking was sufficient for phase stable photon echo experiments to be conducted. Three experiments are presented in this thesis. The first experiment involved the characterization of the detection mode and the two pulse photon echo. Benchmark values are given to the photon echo efficiency, echo lifetime and Rabi frequency. The second experiment is the characterization of the amplified spontaneous emission from inverting a two level ensemble of cryogenic rare earth ions doped in a solid. These experiments were conducted on different optical depths on the inhomogeneous line of Tm:YAG. We find that indeed there is phase independent noise after the inversion with a bandwidth given by the Fourier width of the inverting pulse. It was seen that the noise measured increased exponentially with the optical depth, as expected from the theoretical analysis. The third experiment was the measurement of rephased amplified spontaneous emission and the nonclassical time separated correlation between the noise and the rephased noise. As outlined by the theory, the amplified spontaneous emission can be rephased with a pi pulse. This experiment is implemented on different optical depths on the inhomogeneously broadened line of Tm:YAG. For optical depths of 0.25 and greater, it was seen that the correlations were classical. For an optical depth of 0.046, the correlation was seen to violate the inseparability criterion. This violation of the criterion means that the ASE and RASE fields can not be described as a separable state. This correlation measurement was made with a confidence interval of 95.15%.
This thesis explores the use of cryogenic rare earth ion doped solids for applications in quantum information science. A theoretical analysis of optically rephased memory protocols, namely the two pulse photon echo, is developed. This analysis is a fully quantum mechanical analysis. The two pulse photon echo suffers from collective amplified spontaneous emission in the output mode due to gain along the direction of propagation. This noise can be 'rephased' with a pi pulse, much like a two pulse photon echo, resulting in time separated nonclassical correlations. This thesis aims to characterize this noise and experimentally realize these nonclassical correlations. A theoretical analysis is presented for a hybrid photon echo rephasing protocol. The protocol uses strong optical rephasing pulses as well as external electric fields to rephase coherence in a two level ensemble of atoms. The Stark effect is utilized to reduce the collective spontaneous emission caused by inversion. We find that the protocol is noise free and has a theoretical maximum efficiency of 54% in the forward direction and 100% in the backward direction. The necessary task of laser frequency stabilization is presented in this thesis. The laser is locked using electronic and optical feedback, named the 'hybrid' lock. A theoretical analysis is presented as well as experimental results. The laser locking was sufficient for phase stable photon echo experiments to be conducted. Three experiments are presented in this thesis. The first experiment involved the characterization of the detection mode and the two pulse photon echo. Benchmark values are given to the photon echo efficiency, echo lifetime and Rabi frequency. The second experiment is the characterization of the amplified spontaneous emission from inverting a two level ensemble of cryogenic rare earth ions doped in a solid. These experiments were conducted on different optical depths on the inhomogeneous line of Tm:YAG. We find that indeed there is phase independent noise after the inversion with a bandwidth given by the Fourier width of the inverting pulse. It was seen that the noise measured increased exponentially with the optical depth, as expected from the theoretical analysis. The third experiment was the measurement of rephased amplified spontaneous emission and the nonclassical time separated correlation between the noise and the rephased noise. As outlined by the theory, the amplified spontaneous emission can be rephased with a pi pulse. This experiment is implemented on different optical depths on the inhomogeneously broadened line of Tm:YAG. For optical depths of 0.25 and greater, it was seen that the correlations were classical. For an optical depth of 0.046, the correlation was seen to violate the inseparability criterion. This violation of the criterion means that the ASE and RASE fields can not be described as a separable state. This correlation measurement was made with a confidence interval of 95.15%.
This thesis explores the concept of photon-echo-rephasing of the spontaneous emission from an ensemble of atoms. This generates entangled photon pairs, with intermediate storage and on-demand recall of one photon of the pair. In the first instance, this has applications as a single photon source. A more advanced application is as a building-block of a quantum repeater protocol, which is essential for expanding the range and versatility of current quantum communication links. The system used for this experimental demonstration of rephased amplified spontaneous emission (RASE) is a rare-earth ion doped crystal; Pr:YSO. Rare earth ion crystals are promising candidates for practical quantum information processing devices, largely because they possess long coherence times on both optical and hyperfine transitions. To achieve the rephasing, a novel pulse sequence utilizing four atomic levels is developed and characterized. This pulse sequence allows for the single-photon signals to be resolved spatially, spectrally, and temporally from any background coherent emission associated with the bright driving fields. It is seen that spontaneous emission can indeed be rephased using this sequence, however the degree of correlation measured was not sufficient to prove a non-classical correlation. This is attributed to an insufficient signal to noise ratio. The sources of background noise are identified, and strategies proposed to enable improved correlation measurements in future RASE experiments. The most significant noise contribution is spontaneous emission that differs only slightly in frequency from the signal. Single-photon counters are used for the RASE detection; appropriate for discrete-variable quantum repeater applications, but lacking any frequency resolution. Therefore auxiliary frequency filtering is required. Narrow-band (~kHz) filtering is performed in the RASE experiment using spectral hole-burning properties of the Pr:YSO sample itself. Furthermore, a concept for a dynamic filter is developed and tested. This uses a combination of hole-burning and Stark-shifting. The demonstration involves switching between two MHz-wide transmission windows, 10.2 MHz apart. Each spectral region is switched from an absorption of ~0.5 dB to 60 dB in a matter of micro-seconds. This technique will be particularly useful in future RASE experiments for tunable frequency discrimination. An additional noise source that is found to fundamentally limit the fidelity of RASE in this system is due to uncorrelated spontaneous emission at the same frequency as the RASE signal. This emission is a direct consequence of the low branching ratio of the optical transition. A means of avoiding this emission is proposed; namely to place the sample in a cavity to effectively enhance the branching ratio. Aside from the quality of the photon correlations, another important aspect of RASE is the storage time. Methods are discussed for achieving long memory times (~1 s) in the Pr:YSO system, using transitions between ground state hyperfine levels. In general this thesis presents a series of experiments that lay the foundation for generating entanglement between photonic and collective-atomic states, through the measurement and rephasing of spontaneous emission from an ensemble of atoms.
This thesis investigates an entangled light source with an in-built quantum memory based on the protocol of rephased amplified spontaneous emission (RASE). RASE has promising applications as a building-block of a quantum repeater: a device essential for extending the range of current quantum communication links. To be useful RASE must be able to produce high fidelity non-classical light with high efficiency, and be able to store multimode entanglement for long times. This thesis characterises the RASE source and determines to what degree these requirements can be met. The experimental RASE demonstration was conducted in a rare-earth ion doped crystal. Rare-earth ions provide a particularly promising platform for developing quantum technologies as they possess long coherence times on both the optical and hyperfine transitions. In the RASE protocol an inverted ensemble of two-level atoms amplifies the vacuum fluctuations resulting in amplified spontaneous emission (ASE). This results in entanglement between the output optical field and the collective modes of the amplifying ensemble. The collective atomic state dephases due to the inhomogeneous broadening of the ensemble but this can be rephased using photon echo techniques. When the ensemble rephases, a second optical field, the rephased amplified spontaneous emission (RASE), is emitted and is entangled with the ASE. In this thesis, a modified four-level rephasing scheme is used that allows the single photon signals to be spectrally resolved from any coherent background emission associated with the bright driving fields. In addition, four-level RASE incorporates storage on the long-lived hyperfine ground states. Two experiments are described in this thesis. First, a free-space four-level RASE demonstration using continuous-variable detection. In this experiment the different sources of noise were characterised and low noise operation was shown to be possible. Entanglement of the ASE and RASE was confirmed by violating the inseparability criterion with 98.6% confidence. In addition, entanglement was demonstrated after storage of the collective atomic state on the spin states and RASE was shown to be temporally multimode, with almost perfect distinguishability between two temporal modes demonstrated. The degree of entanglement between the ASE and RASE was limited by the rephasing efficiency, which saturated at 3%. It was determined that distortion of the rephasing pulses as they propagate through the optically thick ensemble was the probable cause of the low efficiency. The second experiment was a preliminary cavity-enhanced RASE demonstration. Theoretically perfect rephasing efficiency can be obtained by placing the crystal in an impedance-matched optical cavity. The initial cavity design showed encouraging evidence of an enhancement in the rephasing efficiency, with a 4-fold improvement over the free-space experiment. Improvements to the cavity design were proposed to allow a further increase in the rephasing efficiency of RASE. In summary, this thesis provides an extensive characterisation of an entangled light source with an in-built quantum memory based on rephasing spontaneous emission from an ensemble of ions. Importantly, the RASE scheme allows generation and storage of entanglement in a single protocol, which holds great promise for the development of integrated quantum networks.
It has been proposed that secure communication over large distances can be achieved using quantum repeater protocols. Two key components which are required for a repeater are an entangled light source and a quantum memory. The approach investigated here, is to use a protocol which incorporates both a memory and entangled light source using rephased amplified spontaneous emission (RASE). To be a viable repeater, RASE must achieve second long storage times, and efficiencies exceeding 90%. The focus of this thesis was to investigate the mechanisms limiting the efficiency of RASE. In this work, RASE was performed in the rare-earth ion-doped crystal Pr3+:Y2SiO5, and the coherence was stored on the ground hyperfine transition for 5 µs. Rare-earth ion-doped crystals are an ideal platform for RASE because they offer long optical and hyperfine coherence times. The hyperfine transitions are of particular interest, because the memory storage times required for repeater can be engineered. RASE works by inverting an ensemble of two-level atoms to create the optical gain necessary for amplified spontaneous emission (ASE). Detection of ASE heralds the ensemble into a collective state which is entangled with the emitted field. Because the ensemble is inhomogeneously broadened, the collective state will then begin to dephase. The state can be rephased, after a tunable delay time, and the entanglement readout as a second optical field (RASE). In this work, the metric chosen to confirm entanglement was the inseparability criterion. In previous work, the two emitted fields of light were proven to be entangled with significant confidence, however, the rephasing efficiency was limited to 3% [1]. The explanation for this was a mismatch between the first and second pass of the beam through the crystal, which was the consequence of a retroreflective mirror being positioned incorrectly. In this thesis, the beam mismatch, caused by the position of the mirror, was shown to not affect the RASE experiment. Instead, the RASE experiment is more likely to be affected by a spatial mode mismatch which is caused by the distortion of the control pulses. The effect of these distortions was observed in the efficiency measurement of RASE. According to the theory, the efficiency of RASE should consistently improve with optical depth. Experimentally, however, in the regime where the two fields were entangled, the efficiency was maximized at 8.3% when the optical depth was 0.8. The performance then began to deteriorate when the optical depth exceeded 1. This result, therefore, informs how the RASE experiment should be designed in the future. Specifically, care should be taken to correct for the effects of any spatial mode distortions, in order for RASE to operate at the threshold efficiency required for a quantum repeater.
This thesis describes a number of coherent processes, such as quantum information processing, superradiance and electromagnetically induced transparency, which have been experimentally implemented using rare-earth-ion-doped crystals. The rare-earths are a class of elements that have in common, an atomic structure that allows for very long lifetimes as well as coherence times, both on optical transitions and on spin transitions. These ions can be naturally trapped inside host crystals, and with the phonon vibrations removed by cooling down to cryogenic temperatures (< 4 K), they can be used for a number of different quantum information processes. Most experiments were carried out using PrYSO, but also other crystal types were investigated, such as Nd:YVO4, and La2(WO4)3. The characterization of the ions were done with a variety of methods, including among others, photon echo techniques and electromagnetically induced transparency. Quantum computing is a rapidly growing field and there are still many potential candidates for its implementation. In our work we have utilized the spin states of the Pr rare-earth ion as a qubit, and demonstrated arbitrary single qubit gates, which are important pieces towards a quantum computing realization in these systems. Most of the experimental work done for the thesis was carried out using an ensemble approach, that has the advantage of giving a strong readout signal, but for future scaling to multiple qubits, single instances are more promising, which is discussed. Quantum memories are crucial components in applications such as quantum networks and long distance quantum communication. In this thesis, work has been done to investigate how quantum memories can be implemented in rare-earth crystals. In particular, there are two protocols, CRIB and AFC, which were suggested with rare-earth crystals directly in mind, and both of these require high optical depth, for maximum recall efficiency. In this thesis, implications of being in the high optical depth regime, with phenomena such as superradiance, a collective effect that could cause the stored light to be immediately reemitted, and slow light effects that come from performing the storage inside spectrally structured materials, were investigated. In order to carry out the phase-sensitive experiments, a laser system with a very narrow linewidth of ~1 kHz at 606 nm was constructed, by locking the laser to a semi-persistent spectral hole. In addition, many experiments required advanced pulse shapes, such as complex sechyp pulses or pulses obtained from optimal control theory. In order to be able to accurately create such shapes, an elaborate system using an arbitrary waveform generator and two well calibrated AOMs, controlled from a computer, was also built.
This thesis describes investigations of the use of cryogenically cooled rare-earth-ion-doped crystals for quantum information processing and quantum optics. Several aspects of the coherent interaction between light and rare-earth ions in solids are addressed. Quantum information science has given physicists new views of quantum mechanics. The transmission of quantum states has already found practical use and full scale quantum computers may one day perform computations and simulations that would be impossible on a conventional computer. The work presented in this thesis can be seen as a part of a broad effort to learn how to control and manipulate quantum mechanical systems, which will become necessary as science and technology continue to push ever deeper into the nanoscopic world. Coherent radiation, such as laser light, provides us with an ideal tool for these investigations and, along the way, we may also learn more about the quantum nature of light. Rare-earth ions in inorganic crystals have several unusual properties that are interesting for applications within quantum information science, including long coherence times and long-lived ground state sublevels that can be used for storage of quantum and classical information. As part of the work presented in this thesis, new materials have been investigated with respect to these properties, and ways to enhance the useful properties of the materials were explored. In one investigation, the lifetime of information stored in the ground state population distribution of Tm3 ions in YAG was shown to increase by several orders of magnitude with the application of a magnetic field. It is demonstrated how the optical inhomogeneous absorption profile can be prepared, so that the light only interacts with a selected group of ions, absorbing on a specific transition. Narrow absorbing structures, with widths approaching the optical homogeneous linewidth, have been prepared with no absorption in the surrounding spectral interval. This thesis addresses the use of such structures as hardware for quantum bits. Tailored pulses, capable of inducing controlled changes in the quantum states of the ions (qubits), even in the presence of unknown variations of coupling strengths and frequencies, have been realised experimentally and used for multiple transfer of ions between energy levels. Ion-ion interactions, which can be used for performing quantum logic operations, have been investigated in some detail. Techniques for selecting strongly interacting ions, by transferring weakly interacting ions to auxiliary states, have been demonstrated. A scheme for storing the quantum state of light in a solid, using photon-echo-like techniques, is proposed and analysed. In the proposed scheme, an optical wave packet is absorbed and subsequently re-emitted by an inhomogeneous absorption profile, which is tailored and externally controlled by the application of an electric field Additionally, an accumulated photon echo experiment has been performed using faint optical pulses. The experiment can be viewed as a demonstration of delayed self-interference of a single photon and as a demonstration of how a single photon can act as two of the fields in a photon echo process.
In this thesis, aspects of the use of cryogenically cooled rare-earth-ion-doped crystals in the fields of quantum optics and quantum information processing are addressed. The experiments and theoretical considerations referred to in this thesis are based on the coherent transient interaction between light and the ions in the crystals. A photon echo experiment has been performed where faint optical pulses were accumulated in the crystal. In this experiment, the possibility of single photons acting as two of the optical fields in the photon echo process was investigated. Different aspects on the experiment, which can be viewed as delayed self-interference of a single photon, are discussed in this thesis. A scheme for the possible implementation of quantum information processing in rare-earth-ion-doped crystals is presented. A key feature in this scheme is that small groups of ions, which can be optically manipulated and which interact in a controlled way, can be extracted from a collection of randomly positioned ions in the crystal host. Initial experimental investigations of the scheme, indicating the possibility of implementing quantum gates, are also presented in this thesis. In another experiment, the application of magnetic fields of up to 5 T was seen to increase the lifetime of information stored as frequency-dependent modulation of the population of thulium ions doped into a YAG crystal by several orders of magnitude. This mechanism might be useful in data storage and information processing applications. An experiment in which the same type of crystal was used as the active medium in a photon-echo-based pulse compression experiment, where microsecond long pulses were compressed to nanosecond duration using frequency-chirped light pulses, is also reported in this thesis.