With the introduction of superconducting circuits into the field of quantum optics, many experimental demonstrations of the quantum physics of an artificial atom coupled to a single-mode light field have been realized. Engineering such quantum systems offers the opportunity to explore extreme regimes of light-matter interaction that are inaccessible with natural systems. For instance the coupling strength g can be increased until it is comparable with the atomic or mode frequency omega(a,m) and the atom can be coupled to multiple modes which has always challenged our understanding of light-matter interaction. Here, we experimentally realize a transmon qubit in the ultra-strong coupling regime, reaching coupling ratios of g/omega(m) = 0.19 and we measure multi-mode interactions through a hybridization of the qubit up to the fifth mode of the resonator. This is enabled by a qubit with 88% of its capacitance formed by a vacuum-gap capacitance with the center conductor of a coplanar waveguide resonator. In addition to potential applications in quantum information technologies due to its small size, this architecture offers the potential to further explore the regime of multi-mode ultra-strong coupling.
With the introduction of superconducting circuits into the field of quantum optics, many experimental demonstrations of the quantum physics of an artificial atom coupled to a single-mode light field have been realized. Engineering such quantum systems offers the opportunity to explore extreme regimes of light-matter interaction that are inaccessible with natural systems. For instance the coupling strength g can be increased until it is comparable with the atomic or mode frequency omega(a,m) and the atom can be coupled to multiple modes which has always challenged our understanding of light-matter interaction. Here, we experimentally realize a transmon qubit in the ultra-strong coupling regime, reaching coupling ratios of g/omega(m) = 0.19 and we measure multi-mode interactions through a hybridization of the qubit up to the fifth mode of the resonator. This is enabled by a qubit with 88% of its capacitance formed by a vacuum-gap capacitance with the center conductor of a coplanar waveguide resonator. In addition to potential applications in quantum information technologies due to its small size, this architecture offers the potential to further explore the regime of multi-mode ultra-strong coupling.
Abstract With the introduction of superconducting circuits into the field of quantum optics, many experimental demonstrations of the quantum physics of an artificial atom coupled to a single-mode light field have been realized. Engineering such quantum systems offers the opportunity to explore extreme regimes of light-matter interaction that are inaccessible with natural systems. For instance the coupling strength g can be increased until it is comparable with the atomic or mode frequency ω a , m and the atom can be coupled to multiple modes which has always challenged our understanding of light-matter interaction. Here, we experimentally realize a transmon qubit in the ultra-strong coupling regime, reaching coupling ratios of g / ω m = 0.19 and we measure multi-mode interactions through a hybridization of the qubit up to the fifth mode of the resonator. This is enabled by a qubit with 88% of its capacitance formed by a vacuum-gap capacitance with the center conductor of a coplanar waveguide resonator. In addition to potential applications in quantum information technologies due to its small size, this architecture offers the potential to further explore the regime of multi-mode ultra-strong coupling.
The field of cavity quantum electrodynamics (cavity QED) studies the interaction between light and matter on a fundamental level: a single atom interacts with a single photon. If the atom-photon coupling is larger than any dissipative effects, the system enters the strong-coupling limit. A peculiarity of this regime is the possibility to form coherent superpositions of light and matter excitations - a kind of 'molecule' consisting of an atomic and a photonic contribution. The novel research field of circuit QED extends cavity QED concepts to solid-state based system. Here, a superconducting quantum bit is coupled to an on-chip superconducting one-dimensional waveguide resonator. Owing to the small mode-volume of the resonant cavity, the large dipole moment of the 'artificial atom' and the enormous engineering potential inherent to superconducting quantum circuits, remarkable atom-photon coupling strengths can be realized. This thesis describes the theoretical framework, the development of fabrication techniques and the implementation of experimental characterization techniques for superconducting quantum circuits for circuit QED applications. In particular, we study the interaction between superconducting flux quantum bits and high-quality coplanar waveguide resonators in the strong-coupling limit. Furthermore, we report on the first experimental realization of a circuit QED system operating in the ultrastrong-coupling regime, where the atom-photon coupling rate reaches a considerable fraction of the relevant system frequencies. In these experiments we could observe phenomena that can not be explained within the renowned Jaynes-Cummings model.
Light-Matter Interaction – from Strong to Ultrastrong Coupling in Superconducting Quantum Circuits Rudolf Gross TU Munchen / Walther-Meisner-Institut fur Tieftemperaturforschung Superconducting quantum circuits imple-mented by nanostructured superconduc-tors allow for the investigation of funda-mental quantum phenomena on a macro-scopic scale and the implementation of solid state quantum information systems. A big advantage of superconducting quantum two-level systems (qubits) over natural atoms is their design flexibility and wide tunability by means of external control parameters such as magnetic fields. We address the coupling of superconducting flux qubits [1,2] to on-chip microwave resonators, giv-ing rise to the prospering field of superconducting circuit quantum electrodynamics (c-QED), which allows us to study the fundamental interaction between artificial solid state atoms and single microwave photons as the basis for communicating quantum information. Recently, we succeeded to realize for the first time c-QED systems operating in the ultra-strong coupling re-gime, where the atom-cavity coupling rate reaches a considerable fraction of the atom transi-tion frequency [3]. In this regime new objects are formed consisting of matter and light. We present spectroscopy data on these new objects providing insight into novel phenomena that could not be studied in atom cavity-QED so far. We also address the interplay of multi-photon processes and symmetries in a qubit-resonator system by spectroscopically analyzing a super-conducting qubit-resonator system under oneand two-photon driving [4]. [1] T. Niemczyk et al., Supercond. Sci. Techn. 22, 034009 (2009). [2] F. Deppe et al., PRB 76, 214503 (2007); K. Kakuyanagi, et al., PRL 98, 047004 (2007). [3] T. Niemczyk et al., Nature Physics 6, 772-776 (2010). [4] F. Deppe et al., Nature Physics 4, 686 (2008); T. Niemczyk et al., arXiv:1107.0810v1 (2011). Gastgeber: Prof. Martin Dressel, Universitat Stuttgart, Telefon: 0711 685-64946
Abstract The strength of the coupling between an atom and a single electromagnetic field mode is defined as the ratio of the vacuum Rabi frequency to the Larmor frequency, and is determined by a small dimensionless physical constant, the fine structure constant α=Zvac/2RK α = Z vac / 2 R K . On the other hand, the quantum circuit including Josephson junctions behaving as artificial atoms and it can be coupled to the electromagnetic field with arbitrary strength (Devoret et al. 2007). Therefore, the circuit quantum electrodynamics (circuit QED) is extremely suitable for studying much stronger light-matter interaction.
Waveguide circuit quantum electrodynamics (waveguide circuit QED) studies light-matter interaction with superconducting circuits in one dimension. In circuit QED, natural atoms are replaced by superconducting qubits consisting of a non-linear Josephson junction, resulting in an anharmonic energy spectrum just like real atoms. With superconducting qubits, it is possible to study quantum optical phenomena and reach new regimes hard to achieve with real atoms due to weak coupling to the electromagnetic field. The reduction to one dimension in waveguide QED increases the electromagnetic field's directionality, which results in reduced losses. In this thesis, we first introduce circuit quantisation, giving the basis for the next part, where we investigate a transmon, a charge-insensitive artificial atom, coupled to a semi-infinite transmission line. An atom coupled to a semi-infinite waveguide is referred to as an atom in front of a mirror and is the subject of all appended papers. We proceed by summarising Paper I and III's main results: in Paper I, we investigate the spontaneous emission of a transmon coupled to a semi-infinite transmission line, where we take time-delay effects into account. We find that the system dynamics strongly depend on the coupling strength to the transmission line and the atom's position with respect to the electromagnetic field, leading to the Purcell effect or the convergence to a dark state with finite excitation probability. In the high-impedance regime, which we investigate in Paper III, the properties of the transmon coupled to the high-impedance transmission line change drastically. It becomes highly reflective and creates its own cavity with the mirror, resulting in the emergence of cavity modes and vacuum Rabi oscillations in the spontaneous emission dynamics. In the next chapter of the thesis, we demonstrate how to quantise an electromagnetic field and derive a light-matter interaction Hamiltonian within dipole approximation. We then give an introduction to open quantum systems and derive the quantum-optical master equation in Lindblad form. Furthermore, we introduce the dressed state picture, where the interaction of light and matter is so strong that the individual energy levels of light and matter are no longer separable. Both the quantum optical master equation and the dressed state picture are relevant in Paper II and IV. In Paper II, an experimental collaboration, we perform several experiments to characterise and discriminate different decay rates of a superconducting qubit coupled to the end of a transmission line. One experiment measured the atomic fluorescence spectral density, which shows an asymmetry for off-resonant driving, resulting from pure dephasing: an effect that we explain in more detail in this thesis and Paper II. In Paper IV, we theoretically investigate amplification mechanisms realised by different set-ups of an atom coupled to a semi-infinite waveguide. In the considered systems, the amplification of a probe field happens either due to population inversion between the pure states or dressed states or multi-photon processes. We find that compared to an open waveguide, we can achieve a higher gain in the amplification with a semi-infinite waveguide.
Light-matter interaction between an atom and an electromagnetic resonator is ubiquitous in quantum technologies. Although linear light-matter coupling gσ^x(a^+a^†) can reach the ultrastrong regime g/ω > 10−1, nonlinear light-matter coupling 2χσ^za^†a^ is typically perturbative and limited to χ/ω < 10−2. Nonlinear coupling has the advantage of commuting with the atomic σ^z and photonic a^†a^ Hamiltonian, allowing for fundamental operations such as quantum-non-demolition measurement. Here, we use a superconducting circuit to demonstrate the experimental realization of near-ultrastrong χ/ω = (4.852 ± 0.006) × 10−2. We also show signatures of light-light nonlinear coupling ( χa^†a^b^†b^ ) and χ/2π = 580.3 ± 0.4 MHz matter-matter nonlinear coupling ( 4χσ^z,aσ^z,b ), representing the largest reported ZZ interaction between two coherent qubits. Such advances in the nonlinear coupling strength of light, matter modes enable new physical regimes and could lead to orders of magnitude faster qubit readout and gates. Nonlinear light-matter coupling has applications in quantum technologies, for instance in quantum-non-demolition measurements, but its strength is typically limited. Here the authors demonstrate near-ultrastrong nonlinear light-matter coupling in a superconducting circuit with two transmons and a quarton coupler.