We propose a superconducting circuit to implement a two-photon quantum Rabi model in a solid-state device, where a qubit and a resonator are coupled by a two-photon interaction. We analyze the input-output relations for this circuit in the strong-coupling regime and find that fundamental quantum-optical phenomena are qualitatively modified. For instance, two-photon interactions are shown to yield a single- or two-photon blockade when a pumping field is either applied to the cavity mode or to the qubit, respectively. In addition, we derive an effective Hamiltonian for perturbative ultrastrong two-photon couplings in the dispersive regime, where two-photon interactions introduce a qubit-state-dependent Kerr term. Finally, we analyze the spectral collapse of the multiqubit two-photon quantum Rabi model and find a scaling of the critical coupling with the number of qubits. Using realistic parameters with the circuit proposed, three qubits are sufficient to reach the collapse point.
We propose a superconducting circuit to implement a two-photon quantum Rabi model in a solid-state device, where a qubit and a resonator are coupled by a two-photon interaction. We analyze the input-output relations for this circuit in the strong-coupling regime and find that fundamental quantum-optical phenomena are qualitatively modified. For instance, two-photon interactions are shown to yield a single- or two-photon blockade when a pumping field is either applied to the cavity mode or to the qubit, respectively. In addition, we derive an effective Hamiltonian for perturbative ultrastrong two-photon couplings in the dispersive regime, where two-photon interactions introduce a qubit-state-dependent Kerr term. Finally, we analyze the spectral collapse of the multiqubit two-photon quantum Rabi model and find a scaling of the critical coupling with the number of qubits. Using realistic parameters with the circuit proposed, three qubits are sufficient to reach the collapse point.
Single-photon devices at microwave frequencies are important for applications in quantum information processing and communication in the microwave regime. In this work we describe a proposal of a multioutput single-photon device. We consider two superconducting resonators coupled to a gap-tunable qubit via both its longitudinal and transverse degrees of freedom. Thus, this qubit-resonator coupling differs from the coupling in standard circuit quantum-electrodynamic systems described by the Jaynes-Cummings model. We demonstrate that an effective quadratic coupling between one of the normal modes and the qubit can be induced and this induced second-order nonlinearity is much larger than that for conventional Kerr-type systems exhibiting photon blockade. Assuming that a coupled normal mode is resonantly driven, we observe that the output fields from the resonators exhibit strong sub-Poissonian photon-number statistics and photon antibunching. Contrary to previous studies on resonant photon blockade, the first-excited state of our device is a pure single-photon Fock state rather than a polariton state, i.e., a highly hybridized qubit-photon state. In addition, it is found that the optical state truncation caused by the strong qubit-induced nonlinearity can lead to an entanglement between the two resonators, even in their steady state under the Markov approximation.
General solutions to the quantum Rabi model involve subspaces with an unbounded number of photons. However, for the multiqubit multimode case, we find special solutions with at most one photon for an arbitrary number of qubits and photon modes. Such solutions exist for arbitrary single qubit-photon coupling strength with constant eigenenergy, while still being qubit-photon entangled states. Taking advantage of their peculiarities and the reach of the ultrastrong coupling regime, we propose an adiabatic scheme for the fast and deterministic generation of a two-qubit Bell state and arbitrary single-photon multimode W states with nonadiabatic error less than 1%. Finally, we propose a superconducting circuit design to catch and release the W states, and shows the experimental feasibility of the multimode multiqubit quantum Rabi model.
The full two-photon quantum Rabi model describes the nonlinear coupling between a superconducting qubit and a resonator. It possesses [Formula: see text] symmetry, in contrast to the conventional two-photon quantum Rabi model in cavity quantum electrodynamics systems, which exhibits [Formula: see text] symmetry. Using the su(1,1) Lie algebra and [Formula: see text] symmetry, we derive a transcendental function whose zeros yield the exact eigenvalues. The spectral collapse phenomenon at the critical coupling [Formula: see text] is derived analytically. At [Formula: see text], the model can be mapped to an inverse-square potential well, where an infinite number of bound states approach the threshold energy exponentially. Our results may provide new insights into spectral phenomena in practical experimental realizations of superconducting circuits with nonlinear coupling.
The realization of strong nonlinear coupling between single photons has been a long-standing goal in quantum optics and quantum information science, promising wide impact applications, such as all-optical deterministic quantum logic and single-photon frequency conversion. Here, we report an experimental observation of the strong coupling between a single-photon and a two-photon Fock state in an ultrastrongly-coupled circuit-QED system. This strong nonlinear interaction is realized by introducing a detuned flux qubit working as an effective coupler between two modes of a superconducting coplanar waveguide resonator. The ultrastrong light–matter interaction breaks the excitation number conservation, and an external flux bias breaks the parity conservation. The combined effect of the two enables the strong one–two-photon coupling. Quantum Rabi-like avoided crossing is resolved when tuning the two-photon resonance frequency of the first mode across the single-photon resonance frequency of the second mode. Within this new photonic regime, we observe the thresholdless second harmonic generation for a mean photon number below one. Our results represent a key step towards a new regime of quantum nonlinear optics, where individual photons can deterministically and coherently interact with each other in the absence of any stimulating fields. Systems with strong photon-photon interactions enable advanced quantum optical applications as well as the study of highly correlated light-matter states. Here the authors report strong coupling between single- and two-photon states in a superconducting circuit, enabling a new regime of nonlinear quantum optics.
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
Multi-qubit quantum Rabi model, which is a fundamental model describing light-matter interaction, plays an important role in various physical systems. In this paper, we propose a theoretical method to simulate multi-qubit quantum Rabi model in a circuit quantum electrodynamics system. By means of external transversal and longitudinal driving fields, an effective Hamiltonian describing the multi-qubit quantum Rabi model is derived. The effective frequency of the resonator and the effective splitting of the qubits depend on the external driving fields. By adjusting the frequencies and the amplitudes of the driving fields, the stronger coupling regimes could be reached. The numerical simulation shows that our proposal works well in a wide range of parameter space. Moreover, our scheme can be utilized to generate two-qubit gate, Schrödinger states, and multi-qubit GHZ states. The maximum displacement of the Schrödinger cat states can be enhanced by increasing the number of the qubits and the relative coupling strength. It should be mention that we can obtain high fidelity Schrödinger cat states and multi-qubit GHZ states even the system suffering dissipation. The presented proposal may open a way to study the stronger coupling regimes whose coupling strength is far away from ultrastrong coupling regimes.