We investigate the possibility of achieving the strong coupling regime of cavity quantum electrodynamics using rare-earth-metal-ions as impurities in monolithic optical resonators. We conclude that due to the weak oscillator strengths of the rare-earth-metals, it may be possible but difficult to reach the regime where the single photon Rabi frequency is large compared to both the cavity and atom decay rates. However, reaching the regime where the saturation photon and atom numbers are less than one should be much more achievable. We show that in this ``bad cavity'' regime, transfer of quantum states and an optical phase shift conditional on the state of the atom is still possible and suggest a method for coherent detection of single dopants.
We investigate the possibility of achieving the strong coupling regime of cavity quantum electrodynamics using rare-earth-metal-ions as impurities in monolithic optical resonators. We conclude that due to the weak oscillator strengths of the rare-earth-metals, it may be possible but difficult to reach the regime where the single photon Rabi frequency is large compared to both the cavity and atom decay rates. However, reaching the regime where the saturation photon and atom numbers are less than one should be much more achievable. We show that in this ``bad cavity'' regime, transfer of quantum states and an optical phase shift conditional on the state of the atom is still possible and suggest a method for coherent detection of single dopants.
Rare-earth-ion doped crystals are an interesting system for quantum computing investigations due to their long optical and hyperfine coherence times. In particular, the ground-state coherence times can be longer than one second, which makes them perfect for long-term storage of quantum states. They also have the advantage of being a solid-state system. At present, many of the fundamental requirements for quantum computing have been demonstrated using rare-earth-ions; however, quantum state readout has yet to be achieved. The strong-coupling regime is of great importance in cavity quantum electrodynamics, as in this regime interactions between single atoms and single photons can be realized. Strong coupling thereby provides a method of enabling qubit-qubit interactions. It is desirable to achieve this regime with rare-earth-ion doped resonators, as it would enable on-demand readout of quantum states, a necessity for quantum computing, and provide the scalability required for implementation of quantum networks. This thesis describes the work that has gone into investigating the suitability of rare-earth-ion doped whispering-gallery mode resonators for quantum computing applications. A theoretical analysis of the strong-coupling regime is performed, followed by experiments investigating the properties of ions in resonators, and of new rare-earth-ion materials. A final set of experiments studies a new quantum memory protocol for use with rare-earth-ions. A theoretical investigation is undertaken to determine whether the strong-coupling regime will be attainable with rare-earth-ion doped whispering-gallery mode resonators. Emphasis is given to determining which rare-earth-ion materials will have the best properties when used as resonators. Specific applications of the strong-coupling regime are examined for this system; in particular, whether it will be possible to demonstrate the reversible transfer of quantum states, and detection of single dopants. Experiments are performed, measuring the properties of millimetre-sized Pr3+:Y2SiO5 resonators. Direct measurements of cavity quantum electrodynamics parameters are made using photon echoes, giving good agreement with theoretical predictions. Interactions between the atom and cavity are observed and a theoretical model is presented to describe these effects. Thus, a more realistic picture is obtained of the experimental requirements for achieving the strong-coupling regime. The properties of different rare-earth-ion doped materials are measured and analysed to determine their suitability for quantum computing applications. The spin Hamiltonian parameters of Pr3+:YAG are measured using Raman heterodyne spectroscopy, and then used to find the optical transitions with zero first-order Zeeman shift, as this should allow the coherence time to be extended to a point where this system is useful for resonator applications. Hyperfine transitions with zero first-order Zeeman shift are also calculated for Er3+:Y2SiO5, with the aim of enabling long-term storage in a telecommunication-wavelength memory. The thesis concludes with an experimental investigation into a new quantum memory technique that does not require spectral hole burning. The hybrid photon echo rephasing protocol uses strong optical pulses to perform rephasing, thus utilizing the advantageous properties of the two-pulse photon echo. Furthermore, the use of external broadening fields removes the usual problem of noise from amplified spontaneous emission. The properties of this memory are examined using a Pr3+:Y2SiO5 crystal.
Strong coupling between an emitter and a cavity is fundamental for quantum networks, enabling deterministic quantum state transfer, distributed quantum computing, and on-demand entanglement generation. Rare-earth ions (REIs) are compelling candidates for such networks due to their long optical and spin coherence times. However, their inherently weak intra-4f optical transitions typically result in low coupling strengths, restricting most current achievements to the weak coupling regime. Our work proposes a realistic approach for achieving strong coupling between rare-earth ions and high-Q whispering-gallery-mode (WGM) microcavities. Our simulations further demonstrate that electro-optic tuning in this microdisk resonator system enables precise frequency alignment between rare-earth ions and the optical cavity mode across arbitrary target frequencies. Additionally, we provide numerical validation for a parametric amplification technique to enhance the emitter-cavity coupling strength. As an extension of this approach, the coupled system efficiently achieves the quantum entanglement of local and flying qubits. This study deepens the understanding of emitter-cavity interactions and contributes to realizing REIs-based photonic platforms, which are crucial to distributed quantum computing and developing robust quantum networks.
Strong coupling between an atom and an electromagnetic resonator is an important condition in cavity quantum electrodynamics. While strong coupling in various physical systems has been achieved so far, it remained elusive for single atomic ions. Here, we achieve a coupling strength of 2π×(12.3±0.1) MHz between a single ^{40}Ca^{+} ion and an optical cavity, exceeding both atomic and cavity decay rates which are 2π×11.5 and 2π×(4.1±0.1) MHz, respectively. We use cavity assisted Raman spectroscopy to precisely characterize the ion-cavity coupling strength and observe a spectrum featuring the normal mode splitting in the cavity transmission due to the ion-cavity interaction. Our work paves the way towards new applications of cavity quantum electrodynamics utilizing single trapped ions in the strong coupling regime for quantum optics and quantum technologies.
When an atom is strongly coupled to a cavity, the two systems can exchange a single photon through a coherent Rabi oscillation. This process enables precise quantum-state engineering and manipulation of atoms and photons in a cavity, which play a central role in quantum information and measurement. Recently, a new regime of cavity QED was reached experimentally where the strength of the interaction between light and artificial atoms (qubits) becomes comparable to the atomic transition frequency or the resonance frequency of the cavity mode. Here we show that this regime can strongly modify the concept of vacuum Rabi oscillations, enabling multiphoton exchanges between the qubit and the resonator. We find that experimental state-of-the-art circuit-QED systems can undergo two- and three-photon vacuum Rabi oscillations. These anomalous Rabi oscillations can be exploited for the realization of efficient Fock-state sources of light and complex entangled states of qubits.
Rare-earth ions doped in crystals are renowned for their excellent coherence properties and large inhomogeneous broadening, which make them ideal for quantum interfaces with broadband photons. These properties have made them one of the leading technologies in quantum optical memories and a promising candidate for optical-to-microwave conversion. To take advantage of the full bandwidth of the rare-earth ensemble, one must overcome the decoherence of a broadband collective excitation due to inhomogeneous broadening. To this end, techniques based on controllable rephasing, such as atomic frequency comb (AFC) or controlled reversible inhomogeneous broadening (CRIB) memories, have been developed with great success. Recently, an alternative method was proposed to suppress the decoherence of an inhomogeneous ensemble via strong coupling to a cavity, a phenomenon called cavity protection. This technique has been demonstrated in the microwave domain with an NV spin ensemble, but has not been demonstrated in the optical domain. Here, we demonstrate cavity protection in the optical domain at the single photon level using an ensemble of rare earths ions coupled to a nanophotonic resonator. The reduction in decoherence due to the cavity-protection effect enables transfer of ultrafast (~50 GHz) frequency qubits into the collective ion excitation and retrieval with 98.7% fidelity. Building on these results to transfer these excitations to long-lived spin states would enable broadband, on-demand quantum memories. Furthermore, this works compliments the work done coupling rare-earths to superconducting resonators in the microwave regime with potential for applications in optical-to-microwave transducers.
We perform an investigation into the properties of Pr3+:Y2SiO5 whispering-gallery-mode resonators as a first step toward achieving the strong coupling regime of cavity QED with rare-earth-metal-ion-doped crystals. Direct measurement of cavity QED parameters are made using photon echoes, giving good agreement with theoretical predictions. By comparing the ions at the surface of the resonator to those in the center, it is determined that the physical process of making the resonator does not negatively affect the properties of the ions. Coupling between the ions and resonator is analyzed through the observation of optical bistability and normal-mode splitting.