Observation of a collective mode of an array of transmon qubits

Arrays of transmon qubits coupled to a λ/2 superconducting coplanar waveguide resonator have been studied by microwave spectroscopy. The emergence of a collective mode has been discovered for a cluster of N > 5 qubits, whose coupling constant to the electromagnetic field in the resonator is √N times greater compared to a single qubit. In addition, the emergence of collective multiphoton transitions exciting higher levels of a qubit cluster has been demonstrated and the interaction of an individual qubit with such a cluster has been investigated.     

Photon-number squeezing in circuit quantum electrodynamics

A superconducting single-electron transistor (SSET) coupled to an anharmonic oscillator, e.g., a Josephson junction-L-C circuit, can drive the latter to a nonequilibrium photon-number distribution. By biasing the SSET at the Josephson quasiparticle cycle, cooling of the oscillator as well as a laserlike enhancement of the photon number can be achieved. Here, we show that the cutoff in the quasiparticle tunneling rate due to the superconducting gap, in combination with the anharmonicity of the oscillator, may create strongly squeezed photon-number distributions. For low dissipation in the oscillator, nearly pure Fock states can be produced.     

Sideband transitions and two-tone spectroscopy of a superconducting qubit strongly coupled to an on-chip cavity

Sideband transitions are spectroscopically probed in a system consisting of a Cooper pair box strongly but nonresonantly coupled to a superconducting transmission line resonator. When the Cooper pair box is operated at the optimal charge bias point, the symmetry of the Hamiltonian requires a two-photon process to access sidebands. The observed large dispersive ac-Stark shifts in the sideband transitions induced by the strong nonresonant drives agree well with our theoretical predictions. Sideband transitions are important in realizing qubit-photon and qubit-qubit entanglement in the circuit quantum electrodynamics architecture for quantum information processing.     

Noise-enabled precision measurements of a duffing nanomechanical resonator

We report quantitative measurements of the nonlinear response of a radio frequency mechanical resonator with a very high quality factor. We measure the noise-free transitions between the two basins of attraction that appear in the nonlinear regime, and find good agreement with theory. We measure the transition rate response to controlled levels of white noise, and extract the basin activation energy. This allows us to obtain precise values for the relevant frequencies and the cubic nonlinearity in the Duffing oscillator, with applications to parametric sensing.     

Intracavity correlation of light in two-wavelength laser

Correlation of light intensity of two laser lines has been observed as a function of the position in the resonator of a He-Ne laser operating on two cascading transitions - 3.39 μm and 7.69 μm. The variation of the two-photon correlation along the cavity has been found to be distinguishably different from that of the product of intensities. The obtained results depend on the propagation conditions of the 3.39 μm line and are most interesting in the case of a one-mirror resonator for this beam. The experimental data show that a mutual interaction between beams is realized not only by mean intensities, but also by their correlation.     

Frequency shifts in a cesium atomic clock due to Majorana transitions

This paper deals with a theoretical model which describes the effect of Majorana transitions on the frequency of a cesium atomic clock. In contrast to the explanations given in the past, the phase correlation between the individual successive excitations in inhomogeneous magnetic fields and the microwave resonator are for the first time taken into account. The π transitions with the selection rule ΔF = 1, Δm = ± 1 are of particular importance. The theory allows experimental results obtained in the past with the CSX apparatus, in particular the large frequency shifts observed, to be interpreted. The effect on the determination of the uncertainty of primary atomic clocks will be discussed.     

A rubidium-stabilized ring-cavity resonator for optical frequency metrology: precise measurement of the D1 line in 133Cs

We have developed a ring-cavity resonator that can be used to measure the absolute frequencies of optical transitions with an uncertainty below 40 kHz. The length of the resonator is calibrated against a reference laser locked to the D₂ line of ⁸⁷Rb, the frequency of which is known with 6 kHz accuracy. We demonstrate the power of this technique by measuring the absolute frequencies of various hyperfine transitions in the D₁ line of ¹³³Cs. Our results agree with earlier measurements using the frequency-comb technique, and have similar accuracy. Measurement of the D₁-line frequency could lead to a more precise determination of the fine-structure constant. We also report a precise value of A=291.918(8) MHz for the hyperfine constant in the 6P_1/2 state.     

Cooling trapped atoms in optical resonators

We derive an equation for the cooling dynamics of the quantum motion of an atom trapped by an external potential inside an optical resonator. This equation has broad validity and allows us to identify novel regimes where the motion can be efficiently cooled to the potential ground state. Our result shows that the motion is critically affected by quantum correlations induced by the mechanical coupling with the resonator, which may lead to selective suppression of certain transitions for the appropriate parameters regimes, thereby increasing the cooling efficiency.     

Self oscillations of a bistable element in two coupled hybrid ring resonators

A CdS crystal showing thermally induced optical bistability is incorporated into two coupled hybrid ring resonators with different delay times. Both delay times are much longer than the relaxation time of the nonlinearity. The resulting self-oscillations are investigated both experimentally and theoretically. We find two different types of oscillation modes. If the crystal is on the lower branch of the bistability during the longer delay time, step like oscillations similar to the case of a single resonator occur. If the crystal is in the lower state onlh for the shorter delay time (also the shorter of the two delay times is much longer than the relaxation time) we find more complicated modes with plateaus and stairs because the long resonator acts as a memory for the system state before the switching process. We find complex mode locking structures exhibiting Farey-tree like transitions between different oscillation modes as well as mode coexistence. Based on an adiabatic theory we compute the regions of extstence of the different oscillation modes and compare them with experimental results.     

Realization of a continuous frequency-tuning Ti:sapphire laser with an intracavity locked etalon

A continuous-wave all-solid-state tunable Ti:sapphire laser with compact configuration is presented. The frequency-tuning range extends from 760 to 825 nm by rotating the birefringent filters. When the intracavity etalon is locked on the oscillating frequency of the laser and the length of the resonator is scanned by the piezoelectric ceramics transducer, a maximal continuous frequency-tuning range of 15.3 GHz is realized. The obtained Ti:sapphire laser is successfully applied to scan the saturation absorption spectroscopy of D1 transitions of87Rb atoms around the wavelength of 794.97 nm.     

Chaos in generalized Jaynes-Cummings model

The possibility of chaos formation is studied in terms of a generalized Jaynes-Cummings model which is a key model in the quantum electrodynamics of resonators. In particular, the dynamics of a three-level optical atom which is under the action of the resonator field is considered. The specific feature of the considered problem consists in that not all transitions between the atom levels are permitted. This asymmetry of the system accounts for the complexity of the problem and makes it different from the three-level systems studied previously. We consider the most general case, where the interaction of the system with the resonator depends on the system coordinate inside the resonator. It is shown that, contrary to the commonly accepted opinion, the absence of resonance detuning does not guarantee the system state controllability. In the course of evolution the system performs an irreversible transition from the purely quantum-mechanical state to the mixed state. It is shown that the asymmetry of the system levels accounts for the fact that the upper excited level turns out to be the most populated one.     

Precise frequency measurements of atomic transitions by use of a Rb-stabilized resonator

We demonstrate a technique for frequency measurements of atomic transitions with a precision of 30 kHz. The frequency is measured with a ring-cavity resonator whose length is calibrated against a reference laser locked to the D2 line of 87Rb, the frequency of which is known with 10-kHz accuracy. We have used this method to measure the hyperfine structure in the 5P(3/2) state of 85Rb. We obtain precise values for the hyperfine constants, A = 25.041(6) MHz and B = 26.013(25) MHz, and a value of 77.992(20) MHz for the isotope shift in the D2 line.     

Quantum dynamics of a mechanical resonator driven by a cavity

We explore the quantum dynamics of a mechanical resonator whose position is coupled to the frequency of an optical (or microwave) cavity mode. When the cavity is driven at a frequency above resonance the mechanical resonator can gain energy and for sufficiently strong coupling this results in limit-cycle oscillations. Using a truncated Wigner function approach, which captures the zero-point fluctuations in the system, we develop an approximate analytic treatment of the resonator dynamics in the limit-cycle regime. We find that the limit-cycle oscillations produced by the cavity are associated with rather low levels of energy fluctuations in the resonator. Compared to a resonator at the same temperature which is driven by a pure harmonic drive to a given average energy, the cavity-driven oscillations can have much lower energy fluctuations. Furthermore, at sufficiently low temperatures, the cavity can drive the resonator into a non-classical state which is number-squeezed.     

A model describing the single and multiple line spectra of tunable microcrystal lasers

A theoretical model is derived by which the occurrence of the single and multiple emission line spectra of tunable microcrystal lasers is described. These spectra in general exhibit several emission lines, arising from the Stark-split atomic levels of the lasing ions in the crystal field. The model is based on the shift of the resonator frequencies due to the thermally induced shift of the optical resonator length and demonstrates that the coincidence of the resonator frequencies with the laser gain lines leads to the emission of single or multiple line spectra of microcrystal lasers. These spectra can be described by the model. The model is given as a set of criteria. In this way not only can predictions of the single emission-line tuning range be made but also resonator lengths can be optimized in order to obtain a maximum tuning range. Furthermore, Q-switched operation can be achieved for specific parameters by periodically shifting the resonator frequencies. The linewidth of the gain used in this model depends on the laser threshold and is folded with the thermal shift of the atomic transitions. Therefore the centre wavelength of the gain is assumed to be constant. The advantage is that this experimentally relevant linewidth can be measured easily with microcrystal lasers themselves, whereas spectroscopic data do not take laser threshold behaviour into account. It is shown that the results of the model are in good agreement with experimental data measured for two different Nd: YAG crystals. Simply by inserting other material and laser parameters, the model can easily be applied to other laser crystals and other wavelengths.     

The scattering cross section of a resonator in a multimode waveguide

The scattering of sound by a single monopole-dipole resonator in a multimode pipe is investigated. The resonator has the form of a Helmholtz resonator connected through a small bar to the pipe wall. In fact, this resonator is a combination of a monopole resonator and a dipole one positioned at the same point. The scattered fields of these resonators are orthogonal to each other. The scattering cross sections of the monopole and dipole resonators in a multimode pipe are calculated. The scattering cross section of the monopole-dipole resonator is determined as the sum of the scattering cross sections of the monopole and the dipole resonators. The friction in a resonator (the monopole or dipole resonator) reduces its scattering cross section by a factor of (1 + β)², where β is the ratio between the friction resistance and the radiation resistance of this resonator.     

Dipole coupling of a double quantum dot to a microwave resonator

We demonstrate the realization of a hybrid solid-state quantum device, in which a semiconductor double quantum dot is dipole coupled to the microwave field of a superconducting coplanar waveguide resonator. The double dot charge stability diagram extracted from measurements of the amplitude and phase of a microwave tone transmitted through the resonator is in good agreement with that obtained from transport measurements. Both the observed frequency shift and linewidth broadening of the resonator are explained considering the double dot as a charge qubit coupled with a strength of several tens of MHz to the resonator.     

Infrared imaging as a means of visually characterizing the thermoacoustic onset process influenced by a Helmholtz resonator

A Helmholtz resonator can be used as a transmission part to connect the thermoacoustic engine (TE) with its load. However, the resonator can significantly influence the performance of the TE. In order to investigate the impact of a Helmholtz resonator on the onset process of a TE, infrared (IR) imaging is firstly used as a visualization method to characterize the onset mechanism. The influence of dimensions of the Helmholtz resonator on the onset process are analyzed experimentally and theoretically. Results show that the Helmholtz resonator reduces the pressure amplitude at the onset moment and increases the onset temperature of the TE, both of which depend on the acoustic power absorbed from the TE. Onset without a sudden increase of pressure amplitude is observed with the Helmholtz resonator at resonance length. This paper shows that IR imaging is an effective way to characterize the temperature distribution in a TE study.     

Pulsed first-overtone CO laser: effective source of IR radiation in spectral range of 2.5–4.0 μm

Spectral properties of radiation of a pulsed electron-beam controlled discharge laser operating on the first-overtone transitions (Δv=2) of CO molecules have been studied both experimentally and theoretically. Various sets of dielectric mirrors with high reflectivity in the wide range of overtone spectrum have been used for the laser resonator. Multiwavelength lasing has been obtained in the wide spectral range of 2.5–4.0 μm. Efficiency of the laser operating on few vibrational transitions within a relatively narrow spectral range comes up to 5% at entirely suppressed fundamental band (Δv=1) lasing. Spectral characteristics of the overtone laser operating on a selected set of vibrational transitions have been analyzed theoretically. A comparison of the experimental and theoretical data has been made.     

Open-type EPR spectrometer to measure electron spins of a sample located outside a resonator

An open-type electron paramagnetic resonance (EPR) spectrometer to measure a sample located outside a resonator was fabricated. As the resonator, the field modulation coils, and the main magnet were integrated on the resonator side in the sensor head, the space for a sample was opened. Thus, a large sample could be placed at the end of the resonator without much limitation on the size. For an application of this apparatus, various coal masses were placed on the resonator of the sensor head and EPR measurements were performed nondestructively. It was found that the EPR signal intensity of coals showed a good correlation with the carbon-to-hydrogen ratio, one of the parameters for classifying coal.     

Cooling of a nanomechanical resonator in presence of a single diatomic molecule

We propose a theoretical scheme for coupling a nanomechanical resonator to a single diatomic molecule via microwave cavity mode of a driven LC$LC$ resonator. We describe the diatomic molecule by a Morse potential and find the corresponding equations of motion of the hybrid system by using Fokker–Planck formalism. Analytical expressions for the effective frequency and the effective damping of the nanomechanical resonator are obtained. We analyze the ground state cooling of the nanomechanical resonator in presence of the diatomic molecule. The results confirm that presence of the molecule improves the cooling process of the mechanical resonator. Finally, the effect of molecule’s parameters on the cooling mechanism is studied.