We control transition frequency of a superconducting flux qubit coupled to a frequency-tunable resonator comprising a direct current superconducting quantum interference device (dc-SQUID) by microwave driving. The dc-SQUID mediates the coupling between microwave photons in the resonator and a flux qubit. The polarity of the frequency shift depends on the sign of the flux bias for the qubit and can be both positive and negative. The absolute value of the frequency shift becomes larger by increasing the photon number in the resonator. These behaviors are reproduced by a model considering the magnetic interaction between the flux qubit and dc-SQUID. The tuning range of the transition frequency of the flux qubit reaches $\approx$ 1.9 GHz, which is much larger than the ac Stark/Lamb shift observed in the dispersive regime using typical circuit quantum electrodynamics devices.
We realize a superconducting circuit analog of the generic cavity-optomechanical Hamiltonian by longitudinally coupling two superconducting resonators, which are an order of magnitude different in frequency. We achieve longitudinal coupling by embedding a superconducting quantum interference device (SQUID) into a high frequency resonator, making its resonance frequency depend on the zero point current fluctuations of a nearby low frequency LC-resonator. By employing sideband drive fields we enhance the intrinsic coupling strength of about 15 kHz up to 280 kHz by controlling the amplitude of th…
We propose a quantum non-demolition Majorana qubit readout protocol based on parametricmodulation of a longitudinal interaction between a pair of Majorana bound states and a resonator. The interaction can be modulated through microwave frequency gate-voltage or flux control of a tunable tunnel barrier. The qubit-resonator coupling is quantum non-demolition to exponential accuracy, a property inherited from the topological nature of the Majorana zero modes. The same mechanism as used for single-qubit readout can also be extended to perform multi-qubit measurements and be used to enact long rang…
Quantum thermal transport and two-photon statistics serve as two representative nonequilibrium features in circuit quantum electrodynamics systems. Here, we investigate quantum heat flow and two-photon correlation function at steady-state in a composite qubit-resonator model, where one qubit shows both transverse and longitudinal couplings to a single-mode optical resonator. With weak qubit-resonator interaction, we unravel two microscopic transport pictures, i.e., cotunneling and cyclic heat exchange processes, corresponding to transverse and longitudinal couplings respectively. At strong qub…
Long-distance two-qubit coupling, mediated by a superconducting resonator, is a leading paradigm for performing entangling operations in a quantum computer based on spins in semiconducting materials. Here, we demonstrate a novel, controllable spin-photon coupling based on a longitudinal interaction between a spin qubit and a resonator. We show that coupling a singlet-triplet qubit to a high-impedance superconducting resonator can produce the desired longitudinal coupling when the qubit is driven near the resonator's frequency. We measure the energy splitting of the qubit as a function of the d…
We present a circuit construction for a new fixed-frequency superconducting qubit and show how it can be scaled up to a grid with strictly local interactions. The circuit QED realization we propose implements $σ_z$-type coupling between a superconducting qubit and any number of $LC$ resonators. The resulting \textit{longitudinal coupling} is inherently different from the usual $σ_x$-type \textit{transverse coupling}, which is the one that has been most commonly used for superconducting qubits. In a grid of fixed-frequency qubits and resonators with a particular pattern of always-on interaction…
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 multi-output 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 mo…
Microwave-frequency superconducting resonators are ideally suited to perform dispersive qubit readout, to mediate two-qubit gates, and to shuttle states between distant quantum systems. A prerequisite for these applications is a strong qubit-resonator coupling. Strong coupling between an electron-spin qubit and a microwave resonator can be achieved by correlating spin- and orbital degrees of freedom. This correlation can be achieved through the Zeeman coupling of a single electron in a double quantum dot to a spatially inhomogeneous magnetic field generated by a nearby nanomagnet. In this pape…
Optomechanical systems typically use light to control the quantum state of a mechanical resonator. In this paper, we propose a scheme for controlling the quantum state of light using the mechanical degree of freedom as a controlled beam splitter. Preparing the mechanical resonator in non-classical states enables an optomechanical Stern-Gerlach interferometer. When the mechanical resonator has a small coherent amplitude it acts as a quantum control, entangling the optical and mechanical degrees of freedom. As the coherent amplitude of the resonator increases, we recover single photon and two-ph…
We introduce a new hybrid qubit consisting of a Majorana qubit interacting with a transmon longitudinally coupled to a resonator. To do so, we equip the longitudinal transmon qubit with topological quasiparticles, supported by an array of heterostructure nanowires, and derive charge- and phase-based interactions between the Majorana qubit and the resonator and transmon degrees of freedom. Inspecting the charge coupling, we demonstrate that the Majorana self-charging can be eliminated by a judicious choice of charge offset, thereby maintaining the Majorana degeneracy regardless of the quasipart…
We discuss level splitting and sideband transitions induced by a modulated coupling between a superconducting quantum circuit and a nanomechanical resonator. First, we show how to achieve an unconventional time-dependent longitudinal coupling between a flux (transmon) qubit and the resonator. Considering a sinusoidal modulation of the coupling strength, we find that a first-order sideband transition can be split into two. Moreover, under the driving of a red-detuned field, we discuss the optical response of the qubit for a resonant probe field. We show that level splitting induced by modulatin…
Cavity-enhanced radiation-pressure coupling of optical and mechanical degrees of freedom gives rise to a range of optomechanical phenomena, in particular providing a route to the quantum regime of mesoscopic mechanical oscillators. A prime challenge in cavity optomechanics has however been to realize systems which simultaneously maximize optical finesse and mechanical quality. Here we demonstrate for the first time independent control over both mechanical and optical degree of freedom within one and the same on-chip resonator. The first direct observation of mechanical normal mode coupling in …
This thesis is set in the framework of superconducting transmon-type qubit architectures with special focus on two important types of coupling between qubits and harmonic resonators: transverse and longitudinal coupling. We will see that longitudinal coupling offers some remarkable advantages with respect to scalability and readout. This thesis will focus on a design, which combines both these coupling types in a single circuit and provides the possibility to choose between pure transverse and pure longitudinal or have both at the same time. We will start with an introduction to circuit quanti…
We introduce a protocol capable of generating a general measurement operator for a mechanical resonator. The technique requires a qubit-resonator interaction and uses a coherent pulse to drive qubit transitions. This is followed by projective measurement of the qubit's energy, constraining the resonator in a state that depends on the pulse shape. The freedom to choose a pulse shape for the coherent drive enables an arbitrary position-basis measurement operator. Using this measurement operator, we outline a two pulse protocol that probabilistically generates a pure mechanical state with a desir…
We report on the observation of multimode strong coupling of a small ensemble of atoms interacting with the field of a 30-m long fiber resonator containing a nanofiber section. The collective light--matter coupling strength exceeds the free spectral range and the atoms couple to consecutive longitudinal resonator modes. The measured transmission spectra of the coupled atom-resonator system provide evidence of this regime, realized with a few hundred atoms with an intrinsic single-atom cooperativity of 0.26. These results are the starting point for studies in a new setting of light-matter inter…
We propose entangling operations based on the energy curvature couplings of encoded spin qubits to a superconducting cavity, exploring the non-linear qubit response to a gate voltage variation. For a two-qubit ($n$-qubit) entangling gate we explore acquired geometric phases via a time-modulated longitudinal $σ_z$-coupling, offering gate times of 10s of ns even when the qubits and the cavity are far detuned. No dipole moment is necessary: the qubit transverse $σ_x$-coupling to the resonator is zero at the full sweet spot of the encoded spin qubit of interest (a triple quantum dot three-electron…
The dynamical Lamb effect is predicted to arise in superconducting circuits when the coupling of a superconducting qubit with a resonator is periodically switched "on" and "off" nonadiabatically. We show that by using a superconducting circuit which allows to switch between longitudinal and transverse coupling of a qubit to a resonator, it is possible of to observe the dynamical Lamb effect. {The switching between longitudinal and transverse coupling can be achieved by modulating the magnetic flux through the circuit loops.} By solving the Schrödinger equation for a qubit coupled to a resonato…
Frequency mixing in ferrimagnetic resonators based on yttrium and calcium vanadium iron garnets (YIG and CVBIG) is employed for studying their nonlinear interactions. The ferrimagnetic Kittel mode is driven by applying a pump tone at a frequency close to resonance. We explore two nonlinear frequency mixing configurations. In the first one, mixing between a transverse pump tone and an added longitudinal weak signal is explored, and the experimental results are compared with the predictions of the Landau-Zener-Stuckelberg model. In the second one, intermodulation measurements are employed by mix…
We investigate steady-state thermal transport and photon statistics in a nonequilibrium hybrid quantum system, in which a qubit is longitudinally and quadratically coupled to an optical resonator. Our calculations are conducted with the method of the quantum dressed master equation combined with full counting statistics. The effect of negative differential thermal conductance is unravelled at finite temperature bias, which stems from the suppression of cyclic heat transitions and large mismatch of two squeezed photon modes at weak and strong qubit-resonator hybridizations, respectively. The gi…
We investigate the steady-state cooling dynamics of vibrational degrees of freedom related to a nanomechanical oscillator coupled with a laser-pumped quantum dot in an optical resonator. Correlations between phonon-cooling and quantum-dot photon emission processes occur respectively when a photon laser absorption together with a vibrational phonon absorption is followed by photon emission in the optical resonator. Therefore, the detection of photons generated in the cavity mode concomitantly contribute to phonon cooling detection of the nanomechanical resonator.
Collective light shifts of many longitudinal cavity modes induced by coupling to a cold-atom ensemble
Institute of Physics, Centre for Advanced Laser Techniques (CALT)（物理研究所，先进激光技术研究中心）；Institute for Theoretical Physics, Vienna University of Technology (TU Wien)（维也纳工业大学理论物理研究所）
We present a method to identify the coupled, normal modes of a superconducting transmission-line with an embedded lumped element circuit. We evaluate the effective transmission-line non-linearities in the case of Kerr-like Josephson interactions in the circuit and in the case where the embedded circuit constitutes a qubit degree of freedom, which is Rabi coupled to the field in the transmission-line. Our theory quantitatively accounts for the very high and positive Kerr non-linearities observed in a recent experiment [M. Rehák et.al., Appl. Phys. Lett. 104, 162604], and we can evaluate the acc…
Phonon blockade is a purely quantum phenomenon, analogous to Coulomb and photon blockades, in which a single phonon in an anharmonic mechanical resonator can impede the excitation of a second phonon. We propose an experimental method to realize phonon blockade in a driven harmonic nanomechanical resonator coupled to a qubit, where the coupling is proportional to the second-order nonlinear susceptibility $χ^{(2)}$. This is in contrast to the standard realizations of phonon and photon blockade effects in Kerr-type $χ^{(3)}$ nonlinear systems. The nonlinear coupling strength can be adjusted conve…
We report the first observation of low power drive level sensitivity, hyperparametric amplification, and single-mode hyperparametric oscillations in a dielectric rutile whispering-gallery mode resonator at 4.2 K. The latter gives rise to a comb of sidebands at 19.756 GHz. Whereas, most frequency combs in the literature have been observed in optical systems using an ensemble of equally spaced modes in microresonators or fibers, the present work represents generation of a frequency comb using only a single-mode. The experimental observations are explained by an additional 1/2 degree-of-freedom o…
We systematically study the influence of simultaneously modulating the input laser intensity and quantum dot (QD) resonance frequecy on the mean-field dynamics, fluctuation energy transfer and entanglement in a optomechanical semi-conductor resonator embedded with a QD. We show that the modulation and the hybrid system can be engineered to attain the desired mean-field values, control the fluctuation energy transfer and the entanglement between the various degrees of freedom. A remarkably high degree of entanglement can be achieved by modulating only the QD frequency. The interplay between the…
Electromagnetic fields carry momentum, which upon reflection on matter gives rise to the radiation pressure of photons. The radiation pressure has recently been utilized in cavity optomechanics for controlling mechanical motions of macroscopic objects at the quantum limit. However, because of the weakness of the interaction, attempts so far had to use a strong coherent drive to reach the quantum limit Therefore, the single-photon quantum regime, where even the presence of a totally off-resonant single photon alters the quantum state of the mechanical mode significantly, is one of the next mile…
Fast, high-fidelity single and two-qubit gates are essential to building a viable quantum information processor, but achieving both in the same system has proved challenging for spin qubits. We propose and analyze an approach to perform a long-distance two-qubit controlled phase (CPHASE) gate between two singlet-triplet qubits using an electromagnetic resonator to mediate their interaction. The qubits couple longitudinally to the resonator, and by driving the qubits near the resonator's frequency they can be made to acquire a state-dependent geometric phase that leads to a CPHASE gate independ…
Spin-mechanics studies interactions between spin systems and mechanical vibrations in a nanomechanical resonator and explores their potential applications in quantum information processing. In this tutorial, we summarize various types of spin-mechanical resonators and discuss both the cavity-QED-like and the trapped-ion-like spin-mechanical coupling processes. The implementation of these processes using negatively charged nitrogen vacancy and silicon vacancy centers in diamond is reviewed. Prospects for reaching the full quantum regime of spin-mechanics, in which quantum control can occur at t…
We report on an integrated non-degenerate narrowband photon pair source produced at 890 nm and 1320nm via type II parametric down-conversion in a periodically poled waveguide with high-reflective dielectric mirrors deposited on the waveguide end faces. The conversion spectrum consists of three clusters and only 3 to 4 longitudinal modes with about 150 MHz bandwidth in each cluster. The high conversion efficiency in the waveguide, together with the spectral clustering in the double resonator, leads to a high brightness of $3\times10^3~$pairs/(s$\cdot$mW$\cdot$MHz). The compact and rugged monoli…
Microring resonators are attractive for low-power frequency conversion via Bragg-scattering four-wave-mixing due to their comb-like resonance spectrum. However, conversion efficiency is limited to 50% due to the equal probability of up- and down-conversion. Here, we demonstrate how two coupled microrings enable highly directional conversion between the spectral modes of one of the rings. An extinction between up- and down-conversion of more than 40 dB is experimentally observed. Based on this method, we propose a design for on-chip multiplexed single-photon sources that allow localized frequen…
Plasmonic dimer cavities can induce extreme electric-field hot spots that allow one to access ultrastrong coupling regimes using Raman-type spectroscopy on single vibrating molecules. Using a generalized master equation, we study resonant Raman scattering in the strong coupling regime of cavity-QED, when also in the vibrational ultrastrong coupling regime, leading to "phonon-dressed polaritons". The master equation rigorously includes spectral baths for the cavity and vibrational degrees of freedom, as well as a pure dephasing bath for the resonant two-level system, which play a significant ro…
Nitrogen-Vacancy (NV) centers in diamond are attractive tools for sensing and quantum information. Realization of this potential requires effective tools for controlling the spin degree of freedom by microwave (mw) magnetic fields. In this work we present a planar microwave resonator optimized for microwave-optical double resonance experiments on single nitrogen-vacancy (NV) centers in diamond. It consists of a piece of wide microstrip line which is symmetrically connected to two 50 $Ω$ microstrip feed lines. In the center of the resonator, an $Ω$-shaped loop focuses the current and the mw mag…
It is shown that an algebraically defined holographic projection of a QFT onto the lightfront changes the local quantum properties in a very drastic way. The expected ubiquitous vacuum polarization characteristic of QFT is confined to the lightray (longitudinal) direction, whereas operators whose localization is transversely separated are completely free of vacuum correlations. This unexpected ''transverse return to QM'' combined with the rather universal nature of the strongly longitudinal correlated vacuum correlations (which turn out to be described by rather kinematical chiral theories) le…
We describe a method to tune, in-situ, between transverse and longitudinal light-matter coupling in a hybrid circuit-QED device composed of an electron spin degree of freedom coupled to a microwave transmission line cavity. Our approach relies on periodic modulation of the coupling itself, such that in a certain frame the interaction is both amplified and either transverse, or, by modulating at two frequencies, longitudinal. The former realizes an effective simulation of certain aspects of the ultra-strong coupling regime, while the latter allows one to implement a longitudinal readout scheme …
Hybrid devices based on the superconducting qubits have emerged as a promising platform for controlling the quantum states of macroscopic resonators. The nonlinearity added by a qubit can be a valuable resource for such control. Here we study a hybrid system consisting of a mechanical resonator longitudinally coupled to a transmon qubit. The qubit readout can be done by coupling to a readout mode like in c-QED setup. The coupling between the mechanical resonator and transmon qubit can be implemented by modulation of the SQUID inductance. In such a tri-partite system, we analyze the steady-stat…
We consider a two level system with both a transversal and a longitudinal coupling to the electromagnetic field of a resonator. Using a polaron transformation, this Hamiltonian can be mapped onto a Jaynes-Cummings Hamiltonian with generalized field operators acting on the electromagnetic field in the resonator. In contrast to the usual ladder operators $a$ and $a^\dagger$, these operators exhibit a non-monotous coupling strength with respect to the number $n$ of photons in the resonator. Especially, there are roots of the coupling between qubit and resonator at certain photon numbers $n_0$. We…
We describe a possible implementation of the nanomechanical quantum superposition generation and detection scheme described in the preceding, companion paper [Armour A D and Blencowe M P 2008 New. J. Phys. Submitted]. The implementation is based on the circuit quantum electrodynamics (QED) set-up, with the addition of a mechanical degree of freedom formed out of a suspended, doubly-clamped segment of the superconducting loop of a dc SQUID located directly opposite the centre conductor of a coplanar waveguide (CPW). The relative merits of two SQUID based qubit realizations are addressed, in par…
We study the dynamics of a transmon qubit that is capacitively coupled to an open multimode superconducting resonator. Our effective equations are derived by eliminating resonator degrees of freedom while encoding their effect in the Green's function of the electromagnetic background. We account for the dissipation of the resonator exactly by employing a spectral representation for the Green's function in terms of a set of non-Hermitian modes and show that it is possible to derive effective Heisenberg-Langevin equations without resorting to the rotating wave, two level or Markov approximations…
The staggered quantum walk model on a graph is defined by an evolution operator that is the product of local operators related to two or more independent graph tessellations. A graph tessellation is a partition of the set of nodes that respects the neighborhood relation. Flip-flop coined quantum walks with the Hadamard or Grover coins can be expressed as staggered quantum walks by converting the coin degree of freedom into extra nodes in the graph. We propose an implementation of the staggered model with superconducting microwave resonators, where the required local operations are provided by …
We explore the joint activated dynamics exhibited by two quantum degrees of freedom: a cavity mode oscillator which is strongly coupled to a superconducting qubit in the strongly coherently driven dispersive regime. Dynamical simulations and complementary measurements show a range of parameters where both the cavity and the qubit exhibit sudden simultaneous switching between two metastable states. This manifests in ensemble averaged amplitudes of both the cavity and qubit exhibiting a partial coherent cancellation. Transmission measurements of driven microwave cavities coupled to transmon qubi…
Spin qubits in silicon and germanium quantum dots are promising platforms for quantum computing, but entangling spin qubits over micrometer distances remains a critical challenge. Current prototypical architectures maximize transversal interactions between qubits and microwave resonators, where the spin state is flipped by nearly resonant photons. However, these interactions cause back-action on the qubit, that yield unavoidable residual qubit-qubit couplings and significantly affect the gate fidelity. Strikingly, residual couplings vanish when spin-photon interactions are longitudinal and pho…
Hybrid quantum systems with inherently distinct degrees of freedom play a key role in many physical phenomena. Famous examples include cavity quantum electrodynamics, trapped ions, or electrons and phonons in the solid state. Here, a strong coupling makes the constituents loose their individual character and form dressed states. Apart from fundamental significance, hybrid systems can be exploited for practical purpose, noteworthily in the emerging field of quantum information control. A promising direction is provided by the combination between long-lived atomic states and the accessible elect…
The strong coupling limit of cavity quantum electrodynamics (QED) implies the capability of a matter-like quantum system to coherently transform an individual excitation into a single photon within a resonant structure. This not only enables essential processes required for quantum information processing but also allows for fundamental studies of matter-light interaction. In this work we demonstrate strong coupling between the charge degree of freedom in a gate-detuned GaAs double quantum dot (DQD) and a frequency-tunable high impedance resonator realized using an array of superconducting quan…
We discuss the physical interpretation of the gravity mediated entanglement effect. We show how to read it in terms of quantum reference systems. We pinpoint the single gravitational degree of freedom mediating the entanglement. We clarify why the distinction between longitudinal and transverse degrees of freedom is irrelevant for the interpretation of the results. We discuss the relation between the LOCC theorem and the interpretation of the effect, its different relevance for, respectively, the quantum gravity and quantum information communities, and the reason for the excitement raised by t…
Implementation of quantum information processing faces the contradicting requirements of combining excellent isolation to avoid decoherence with the ability to control coherent interactions in a many-body quantum system. For example, spin degrees of freedom of electrons and nuclei provide a good quantum memory due to their weak magnetic interactions with the environment. However, for the same reason it is difficult to achieve controlled entanglement of spins over distances larger than tens of nanometers. Here we propose a universal realization of a quantum data bus for electronic spin qubits w…
Many proposals for solid-state photonic implementations of quantum information processing utilize high-quality optical resonators to achieve strong coupling between guided fields and heterogeneously incorporated qubits. Given the practical difficulty of accurately placing quantum dots, vacancy centers, or other such atom-like emitters throughout a complex nanophotonic circuit, it would be natural to consider whether high-quality resonators could be used in conjunction with bulk optical nonlinearities to create optically-coupled qubit degrees of freedom via lithographic patterning of a homogene…
