In recent years there has been rapid progress into realising a working universal quantum computer, in particular with the development of chip-based radio frequency ion traps. The next significant leap will come with successfully integrating optical cavities into these ion traps to allow for interaction between remote ions via photons as required for more efficient and scalable quantum networking schemes. Fibre-tip cavities are especially interesting for such applications as they enable highly efficient coupling of photons from the cavity into optical fibres for onward transmission. Here we analyse theoretically and numerically the effects of parallel off-axial misalignment in millimetre scale optical Fabry-Perot cavities. While near-concentric cavity configurations produce the smallest mode waist and thus strongest coupling to a trapped ion, their mode is extremely sensitive to misalignment. Shorter cavities exhibit more robust modes, but at the cost of larger mode waists. For example, for typical experimental parameters (mirror radius of curvature 0.7 mm, mirror diameter 0.140 mm, operation wavelength 850 nm) we find that the cavity lifetime is reduced by a factor 1/e for a misalignment of 0.95 nm for a beam waist of 2.91 um (cavity length of 1.397 mm), which increases to 11.0 nm for a waist of 4.33 um (length of 1.386 mm), and 3.12 um for a waist of 7.38 um (length of 1.273 mm). In the parameter regimes of interest, we derive a simple relation between cavity length, mirror radius, and misalignment sensitivity. Finally, we also consider the effect of mode matching of the misaligned cavity mode with the optical mode of the fibre for efficient cavity to fibre coupling. In conclusion, our model allows us to optimise photon-ion coupling in fibre-tip resonators for quantum information processing in the presence of finite fabrication and alignment tolerances.
In recent years there has been rapid progress into realising a working universal quantum computer, in particular with the development of chip-based radio frequency ion traps. The next significant leap will come with successfully integrating optical cavities into these ion traps to allow for interaction between remote ions via photons as required for more efficient and scalable quantum networking schemes. Fibre-tip cavities are especially interesting for such applications as they enable highly efficient coupling of photons from the cavity into optical fibres for onward transmission. Here we analyse theoretically and numerically the effects of parallel off-axial misalignment in millimetre scale optical Fabry-Perot cavities. While near-concentric cavity configurations produce the smallest mode waist and thus strongest coupling to a trapped ion, their mode is extremely sensitive to misalignment. Shorter cavities exhibit more robust modes, but at the cost of larger mode waists. For example, for typical experimental parameters (mirror radius of curvature 0.7 mm, mirror diameter 0.140 mm, operation wavelength 850 nm) we find that the cavity lifetime is reduced by a factor 1/e for a misalignment of 0.95 nm for a beam waist of 2.91 um (cavity length of 1.397 mm), which increases to 11.0 nm for a waist of 4.33 um (length of 1.386 mm), and 3.12 um for a waist of 7.38 um (length of 1.273 mm). In the parameter regimes of interest, we derive a simple relation between cavity length, mirror radius, and misalignment sensitivity. Finally, we also consider the effect of mode matching of the misaligned cavity mode with the optical mode of the fibre for efficient cavity to fibre coupling. In conclusion, our model allows us to optimise photon-ion coupling in fibre-tip resonators for quantum information processing in the presence of finite fabrication and alignment tolerances.
Scalable quantum information processing requires efficient coupling between stationary qubits (trapped atoms, ions, NV centres, etc.) via “flying” single-photon qubits. Here we investigate the optimisation and integration of fibre-tip microcavities into radiofrequency ion traps to achieve (i) high-fidelity transfer of ion qubits onto single photons, (ii) low-loss coupling of cavity photons into single-mode optical fibre, and (iii) achieving conditions (i) and (ii) without disturbing the ion trap. Our cavities are fabricated by laser micro-machining the ends of optical fibres and subsequent coating with a thin dielectric mirror, giving rise to cavity mirrors with a Gaussian profile. These cavities allow for small mode volume and thus large ion-photon coupling fulfilling requirement (i), while simultaneously providing intrinsic coupling to optical fibres, requirement (ii), as long as mode matching between the cavity mode and the fibre mode can be achieved at the cavity mirror. Using a semi-analytical numerical method, we show that Gaussian-shaped mirrors can in fact be used to enhance ion-photon coupling beyond what is possible with more common spherical cavity mirrors. Ion traps are notoriously sensitive to the presence of dielectric materials such as cavity mirrors near the trap centre, preventing requirement (iii) from being achieved. We performed an extensive numerical study of five different common ion traps to find the optimum configurations for integrating fibre-tip cavities with minimised effects on the trapping potentials. We discuss these results and present simple and effective design rules for realising optimum ion-cavity based quantum networks.
Precise control over internal states of atomic ions in ion traps has been possible for many years enabling high precision spectroscopy of atomic transitions. Trapped ions are suitable candidates for quantum information processing due to their long storage times, low decoherence rates and high readout efficiency. Recent advances in micro-machining fibre optic mirrors and integrated fibre optic-ion trap systems for cavity QED allows one to realise strong coupling between an ion and a cavity mode by reducing the mode volume. For strong ion-cavity coupling, deterministic transfer of quantum states between ions and photons is possible. We have designed and constructed a miniaturised linear Paul trap with an integrated optical cavity, intended for coupling multiple ions to the cavity mode. The RF-electrode separation is 50μm, while the endcap separation is 350μm. The endcap electrodes are narrow tubes of inner diameter 300μm allowing optical fibers through the tubes to form the cavity. The trap depth we calculate to be 650meV for a 10V applied potential at 20MHz. The 4P1⁄2→ 3D3⁄2 transition of the atomic ion 40Ca+ with Γ = 24π × 22MHz can be coupled to an optical fibre Fabry-Perot cavity with length of 380µm, finesse of 33,000 and cavity linewidth k = 2π ×11MHz.The ion-cavity coherent coupling g = 2π × 19:5MHz of this system will put it in single-ion strong coupling regime with cooperativity, C=1.5.
Fiber Fabry-Perot cavities, formed by micro-machined mirrors on the end-facets of optical fibers, are used in an increasing number of technical and scientific applications. Some of the most promising areas of application of these optical micro-resonators with high finesse and small mode volume are in the field of quantum communication and information. The resonator-enhanced light-matter interaction, for instance, provide basis for the realization of efficient optical interfaces between stationary matter-based quantum nodes and flying single-photon qubits. To date fiber Fabry-Perot cavities have been successfully applied in experiments interfacing single photons with a wide range of quantum systems, including cold atoms, ions and solid state emitters as well as quantum optomechanical experiments. Here we address some important practical questions that arise during the experimental implementation of high finesse fiber Fabry-Perot cavities: How can optimal fiber cavity alignment be achieved and how can the efficiency of coupling light from the optical fibers to the cavity mode and vice versa be characterized? How should optical fiber cavities be constructed and stabilized to fulfill their potential for miniaturization and integration into robust scientific and technological devices that can operate outside of dedicated laboratory environments in the future? The first two questions we answer with an analytic mode matching calculation that relates the alignment dependent fiber-to-cavity mode-matching efficiency to the easily measurable dip in the reflected light power at the cavity resonance. Our general analysis provides a simple recipe for the optimal alignment of fiber Fabry-Perot cavities and moreover for the first time explains the asymmetry in their reflective line shapes. The latter question we explore by investigating a novel, intrinsically rigid fiber cavity design that makes use of the high passive stability of a monolithic cavity spacer and employs thermal self-locking and external temperature tuning. The performance of this novel approach is compared to a more traditional, piezomechanically-actuated resonator that is feedback stabilized to a reference laser based on the Pound-Drever-Hall locking technique. Finally, with the application of single photon interfacing in mind we discuss the issue of fiber-generated background photons in Fiber Fabry-Perot cavities. We believe that, due to their simplicity, compactness and robustness, rigid fiber cavities could be a promising solution for miniaturized, integratable and scalable cavity quantum electrodynamic devices and further applications of FFPC with similar requirements.
The research undertaken unites two distinct areas of quantum information processing: single ions stored in radio-frequency traps and single photons in optical fibres. Strings of ions are presently the most successful implementation of quantum computing, with elementary quantum algorithm and quantum simulations realised. The principal challenge in the field is to enhance the quantum processing power by scaling up current devices to larger systems. We pursue one of the most promising strategies: distributed quantum computation in which multiple small-scale ion processors are interlinked by exchanging photonic quantum bits via optical fibres. This requires a coherent quantum interface between ions and photons, mapping ionic to photonic quantum states and vice versa. To maximise fidelity and the success rate of the scheme, the interaction of ions and photons must take place in a microscopic optical cavity with high finesse. To this end, single 40Ca+ were trapped in a radio-frequency ion trap whose trapping electrodes are hollow cylinders. Optical fibres with mirrors machined on the facets are inserted into the electrodes to form a Fabry-Pérot cavity. Because the fibres are shielded by the electrodes the detrimental distortion of the trapping field due to their presence is suppressed and ions can be trapped for several hours. 40Ca+ has a -type energy level scheme wherein the ion is cooled on the 42P1/2 ? 42S1/2 transition and the cavity is tuned to the 42P1/2 ? 32D3/2 transition. This thesis reports the successful coupling of single ions to a high finesse optical fibre based cavity, with coupling strength g = 2p · 4:6 MHz. The cavity has length 367 µm, finesse of 40,000 and linewidth 2k = 2p · 9:4 MHz. In this coupling regime, the enhancement of the ion's emission rate through the Purcell effect was observed. Further, anti-correlation was observed in the emission rates between the P1/2 ? D3/2 and P1/2 ? S1/2 transitions with an effective emission rate suppression of up to 60% in the latter transition. The built system offers greater promises. Once the position in the cavity mode has been optimised we expect to reach the long-sought after strong coupling regime with (g, k, y) = 2p · (12:2; 4:7; 11:2) MHz.
Quantum technology has the potential to change the way we solve many problems in our daily lives. Perhaps the most ambitious quantum technology in development is quantum computers. In the past decade significant progress has been made in the number of qubits within a quantum computer, and this trend seems to be increasing. In this work we look at one particular architecture for quantum computing; the iontrap quantum computer. In this thesis we investigate the integration of this type of quantum computer with fibre tip optical cavities. We numerically analyse the effect of misalignment of these cavities and attempt to find the optimal cavity parameters for integration into the ion-trap quantum computer. This work should provide a useful framework for optimal integration of cavities, and the tolerances to misalignment. This should allow for future ion-trap quantum computer designs to be more efficient and help increase the number of qubits, paving the way to develop a useful universal quantum computer.
One of the most exciting prospects of quantum physics today is to simulate large quantum systems, intractable by classical computation, by connecting many smaller systems together. A cavity-based quantum network of atoms and photons constitutes one such approach, where each cavity interfaces between stationary atomic qubits in a node and photonic qubits travelling along optical fibre channels. For this scheme to work well, the cavity-based interface must be faithful and well-controlled. In this thesis, we construct a fibre-tip Fabry-Pérot cavity by aligning two optical fibre-tips against each other, where each has a concave, mirror-coated surface. Three properties make it highly suitable for interfacing: a small mode volume for strong atom-photon coupling, directly fibre-coupled cavity light, and optical access for trapped atoms. For the latter, we design a scheme that allows for a 2D reconfigurable array of atoms, held in the cavity mode by holographically-generated optical tweezers. Our particular design will allow us to move atoms independently of one another. We find the atom-cavity system parameters for optimal single photon generation, absorption and remote state transfer using V-STIRAP (vacuum-stimulated emission by Raman adiabatic passage). Using master equations and the Nelder-Mead algorithm, we optimise both the parameters and V-STIRAP pulse shapes to do this. We assemble the first fibre cavity formed of two single-mode fibres in ultra-high vacuum. Aligning two single-mode fibres is particularly demanding; we overcome this with an assembly method that gives permanent sub-micron alignment precision, unlike other similar cavities that need realigning using a translation stage. We fully characterise the cavity's parameters, then test it by probabilistically loading atoms from a magneto-optical trap, measuring the Purcell-enhanced fluorescence from the cavity. Altogether, our advances facilitate deterministically controlled, strongly-coupled and networked quantum systems.