J. R. Johansson

Observation of the dynamical Casimir effect in a superconducting circuit

One of the most surprising predictions of modern quantum theory is that the vacuum of space is not empty. In fact, quantum theory predicts that it teems with virtual particles flitting in and out of existence. Although initially a curiosity, it was quickly realized that these vacuum fluctuations had measurable consequences—for instance, producing the Lamb shift of atomic spectra and modifying the magnetic moment of the electron. This type of renormalization due to vacuum fluctuations is now central to our understanding of nature. However, these effects provide indirect evidence for the existence of vacuum fluctuations. From early on, it was discussed whether it might be possible to more directly observe the virtual particles that compose the quantum vacuum. Forty years ago, it was suggested that a mirror undergoing relativistic motion could convert virtual photons into directly observable real photons. The phenomenon, later termed the dynamical Casimir effect, has not been demonstrated previously. Here we observe the dynamical Casimir effect in a superconducting circuit consisting of a coplanar transmission line with a tunable electrical length. The rate of change of the electrical length can be made very fast (a substantial fraction of the speed of light) by modulating the inductance of a superconducting quantum interference device at high frequencies (>10 gigahertz). In addition to observing the creation of real photons, we detect two-mode squeezing in the emitted radiation, which is a signature of the quantum character of the generation process.

QuTiP 2: A Python framework for the dynamics of open quantum systems

Abstract We present version 2 of QuTiP, the Quantum Toolbox in Python. Compared to the preceding version [J.R. Johansson, P.D. Nation, F. Nori, Comput. Phys. Commun. 183 (2012) 1760.], we have introduced numerous new features, enhanced performance, and made changes in the Application Programming Interface (API) for improved functionality and consistency within the package, as well as increased compatibility with existing conventions used in other scientific software packages for Python. The most significant new features include efficient solvers for arbitrary time-dependent Hamiltonians and collapse operators, support for the Floquet formalism, and new solvers for Bloch–Redfield and Floquet–Markov master equations. Here we introduce these new features, demonstrate their use, and give a summary of the important backward-incompatible API changes introduced in this version. Program Summary Program title: QuTiP: The Quantum Toolbox in Python Catalog identifier: AEMB_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEMB_v2_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 No. of lines in distributed program, including test data, etc.: 33625 No. of bytes in distributed program, including test data, etc.: 410064 Distribution format: tar.gz Programming language: Python. Computer: i386, x86-64. Operating system: Linux, Mac OSX. RAM: 2+ Gigabytes Classification: 7. External routines: NumPy, SciPy, Matplotlib, Cython Catalog identifier of previous version: AEMB_v1_0 Journal reference of previous version: Comput. Phys. Comm. 183 (2012) 1760 Does the new version supercede the previous version?: Yes Nature of problem: Dynamics of open quantum systems Solution method: Numerical solutions to Lindblad, Floquet–Markov, and Bloch–Redfield master equations, as well as the Monte Carlo wave function method. Reasons for new version: Compared to the preceding version we have introduced numerous new features, enhanced performance, and made changes in the Application Programming Interface (API) for improved functionality and consistency within the package, as well as increased compatibility with existing conventions used in other scientific software packages for Python. The most significant new features include efficient solvers for arbitrary time-dependent Hamiltonians and collapse operators, support for the Floquet formalism, and new solvers for Bloch–Redfield and Floquet–Markov master equations. Restrictions: Problems must meet the criteria for using the master equation in Lindblad, Floquet–Markov, or Bloch–Redfield form. Running time: A few seconds up to several tens of hours, depending on size of the underlying Hilbert space.

QuTiP: An open-source Python framework for the dynamics of open quantum systems !

Article history: We present an object-oriented open-source framework for solving the dynamics of open quantum systems written in Python. Arbitrary Hamiltonians, including time-dependent systems, may be built up from operators and states defined by a quantum object class, and then passed on to a choice of master equation or Monte Carlo solvers. We give an overview of the basic structure for the framework before detailing the numerical simulation of open system dynamics. Several examples are given to illustrate the build up to a complete calculation. Finally, we measure the performance of our library against that of current implementations. The framework described here is particularly well suited to the fields of quantum optics, superconducting circuit devices, nanomechanics, and trapped ions, while also being ideal for use in classroom instruction.

Colloquium: Stimulating uncertainty: Amplifying the quantum vacuum with superconducting circuits

The ability to generate particles from the quantum vacuum is one of the most pro- found consequences of Heisenbergs uncertainty principle. Although the significance of vacuum fluctuations can be seen throughout physics, the experimental realization of vacuum amplification effects has until now been limited to a few cases. Superconducting circuit devices, driven by the goal to achieve a viable quantum computer, may soon be able to realize the elusive verification of the dynamical Casimir effect and analogue Hawking radiation. This article describes several mechanisms for generating photons from the quantum vacuum and emphasizes their connection to the well-known parametric amplifier from quantum optics. Discussed in detail is the possible realization of each mechanism, or its analogue, in superconducting circuit systems. The ability to selectively engineer these circuit devices highlights the relationship between the various amplification mechanisms.

Squeezed optomechanics with phase-matched amplification and dissipation.

We investigate the nonlinear interaction between a squeezed cavity mode and a mechanical mode in an optomechanical system (OMS) that allows us to selectively obtain either a radiation-pressure coupling or a parametric-amplification process. The squeezing of the cavity mode can enhance the interaction strength into the single-photon strong-coupling regime, even when the OMS is originally in the weak-coupling regime. Moreover, the noise of the squeezed mode can be suppressed completely by introducing a broadband-squeezed vacuum environment that is phase matched with the parametric amplification that squeezes the cavity mode. This proposal offers an alternative approach to control the OMS using a squeezed cavity mode, which should allow single-photon quantum processes to be implemented with currently available optomechanical technology. Potential applications range from engineering single-photon sources to nonclassical phonon states.

Landau-Zener-Stückelberg interferometry of a single electron charge qubit

We perform Landau-Zener-Stuckelberg interferometry on a single electron GaAs charge qubit by repeatedly driving the system through an avoided crossing. We observe coherent destruction of tunneling, where periodic driving with specific amplitudes inhibits current flow. We probe the quantum dot occupation using a charge sensor, observing oscillations in the qubit population resulting from the microwave driving. At a frequency of 9 GHz we observe excitation processes driven by the absorption of up to 17 photons. Simulations of the qubit occupancy are in good agreement with the experimental data.

Optomechanical-like coupling between superconducting resonators

We propose and analyze a circuit that implements a nonlinear coupling between two superconducting microwave resonators. The resonators are coupled through a superconducting quantum interference device that terminates one of the resonators. This produces a nonlinear interaction of the standard optomechanical form, where the quadrature of one resonator couples to the photon number of the other resonator. The circuit therefore allows for all-electrical realizations of analogs to optomechanical systems, with coupling that can be both strong and tunable. We estimate the coupling strengths that should be attainable with the proposed device, and we find that the device is a promising candidate for realizing the single-photon strong-coupling regime. As a potential application, we discuss implementations of networks of nonlinearly coupled microwave resonators, which could be used in microwave-photon-based quantum simulation.

Circuit analog of quadratic optomechanics

We propose a superconducting electrical circuit that simulates a quadratic optomechanical system. A capacitor placed between two transmission-line (TL) resonators acts like a semitransparent membrane, and a superconducting quantum interference device (SQUID) that terminates a TL resonator behaves like a movable mirror. Combining these circuit elements, it is possible to simulate a quadratic optomechanical coupling whose coupling strength is determined by the coupling capacitance and the tunable bias flux through the SQUIDs. Estimates using realistic parameters suggest that an improvement in the coupling strength could be realized, to five orders of magnitude from what has been observed in membrane-in-the-middle cavity optomechanical systems. This leads to the possibility of achieving the strong-coupling regime of quadratic optomechanics.

Coupling Two Distant Double Quantum Dots with a Microwave Resonator

We fabricated a hybrid device with two distant graphene double quantum dots (DQDs) and a microwave resonator. A nonlinear response is observed in the resonator reflection amplitude when the two DQDs are jointly tuned to the vicinity of the degeneracy points. This observation can be well fitted by the Tavis-Cummings (T-C) model which describes two two-level systems coupling with one photonic field. Furthermore, the correlation between the DC currents in the two DQDs is studied. A nonzero cross-current correlation is observed which has been theoretically predicted to be an important sign of nonlocal coupling between two distant systems. Our results explore T-C physics in electronic transport and also contribute to the study of nonlocal transport and future implementations of remote electronic entanglement.

Nonclassical microwave radiation from the dynamical Casimir effect

We investigate quantum correlations in microwave radiation produced by the dynamical Casimir effect in a superconducting waveguide terminated and modulated by a superconducting quantum interference device. We apply nonclassicality tests and evaluate the entanglement for the predicted field states. For realistic circuit parameters, including thermal background noise, the results indicate that the produced radiation can be strictly nonclassical and can have a measurable amount of intermode entanglement. If measured experimentally, these nonclassicality indicators could give further evidence of the quantum nature of the dynamical Casimir radiation in these circuits.