Session G25: Itinerant Photons, Squeezed States, and Entanglement

Qubit-Photon Entanglement and Hong-Ou-Mandel Interference with Propagating Microwaves

Itinerant microwave photons offer an attractive carrier of quantum information in superconducting circuits. However, until recently it remained challenging to measure photon statistics and coherence properties of microwave fields beyond the Gaussian level -- mainly due to the absence of efficient detectors in this frequency range. Here, we present the on-demand generation and efficient characterization of microwave radiation and its entanglement with stationary qubits. Based on novel tomography techniques and low noise parametric amplification we are able to resolve all relevant quantum correlations between the propagating field and the superconducting qubit to demonstrate entanglement with high fidelity [1,2]. We have also created entangled microwave fields traveling in two spatially separated modes. Making use of the two-photon interference at a microwave beamsplitter we are able to prepare propagating NOON-type states, which we fully characterize by measuring the joint photon statistics of the two modes. The possibility to synthesize, guide and detect entanglement correlations between itinerant microwave photons and stationary qubits put microwave based quantum network experiments within reach. [1] arXiv:1209.0441v1 [2] C. Eichler et al., Phys. Rev. A 86, 032106 (2012)   

Catching Microwave Photons in a Superconducing Resonator with Tunable Coupling

When transferring a quantum state from a freely propagating mode to a resonator, reflections must be minimized to avoid energy loss. Performing this transfer with high fidelity requires tunable coupling. We experimentally studied a 50 Ohm transmission line with tunable coupling to a 6GHz superconducting coplanar waveguide resonator, which in turn is capacitively coupled to a phase qubit for calibration. We classically drove the resonator while measuring the reflected and captured signals using a HEMT amplifier. Following theory by Korotkov (PRB 84, 014510, 2011), we find that the photon capture efficiency is maximized with an exponentially increasing drive; further improvements come from varying pulse duration and dynamic coupling. With these techniques, we reduce reflections so that presently over 80\% of the pulse energy is captured by the resonator.   

Radiative decay of a superconducting qubit in squeezed vacuum

When the conventional vacuum fluctuations of the electromagnetic environment are replaced by the asymmetric, reduced fluctuations associated with squeezed vacuum, the radiative properties of an atom are predicted to be dramatically altered. We present measurements of the transverse and longitudinal decay rates of a superconducting qubit that couples predominantly to a continuum of squeezed electromagnetic vacuum. We use a lumped element Josephson parametric amplifier to squeeze vacuum fluctuations by up to 10dB with a bandwidth of 20 MHz. The amplifier output is directly coupled to a transmon qubit in a microwave cavity. We observe a dependence of the transverse decay rate on the relative angle between the squeezed axis and the qubit. In particular, at certain angles, we observe an improvement in the qubit T2 time above its nominal value.   

Lossless, coherent Josephson three-wave combiner

We designed and operated a three-wave beam-splitter/combiner, based on Josephson parametric converters, which performs frequency conversion without introducing losses and thus adding no noise to the processed signal. We in particular show that the unitary signal-idler scattering parameters of the device can be fully modulated in-situ by varying the intensity and phase of the pump tone feeding the system. By operating the device as a 50/50 beam-combiner, we interfere coherently two input coherent microwave beams with different frequencies and demonstrate that the resulting interference fringes generated by the relative phase of the pump is in agreement with theoretical predictions. Potential applications of the device include quantum information transduction and realization of an ultra-sensitive interferometer with controllable feedback.   

Extracting Past-Future Vacuum Correlations Using Circuit QED

In this work we propose a realistic circuit QED experiment to test the extraction of past-future vacuum entanglement to a pair of superconducting qubits. A qubit P --for past-- interacts with a quantum field along an open transmission line for an interval $T_{on}$ and then, after a time-lapse $T_{off}$ of no interaction, a second qubit F --for future-- starts interacting for a time $T_{on}$ in a symmetric fashion. After this protocol, past-future quantum correlations will have transferred to the qubits, even if the qubits do not coexist at the same time. We show that this experiment can be realized with current technology and discuss its utility as a possible implementation of a quantum memory.   

Observation of the squeezed state of microwave photon by resolving the even-number Fock states in circuit QED

We theoretically propose an elegant way to detect the microwave parametric down conversion in the circuit QED system. The qubit energy splitting E$_{01}$ is tuned to be quite close to the fundamental frequency $\omega _{1\, }$of the microwave photon and the frequency of the pump beam is chosen to be $\omega_{2}$. We place the qubit at the two-thirds away from the center of the central resonator, which will make the capacitive coupling to the third harmonic mode to be negligible. Since the qubit acts as an optical coupler in our system, one may expect that the following process a$_{2}^{+}$a$_{1}^{+}$a$_{3}$ may appear and compete with the squeezing process a$_{1}^{+}$a$_{1}^{+}$a$_{2}$, which will seriously degrade the quality of squeezing by mixing into the channel. Since the coupling to the third harmonic mode is negligible for our system, we expect instead to observe the clear squeezing of the microwave photon with frequency $\omega _{1}$. We calculate the absorption spectrum of the qubit, which is experimentally measurable and will clearly reveal the squeezed states as the coherent superposition of the even-number Fock states.   

Generation of Nonclassical States of Microwave Radiation via Single Photon Detection

We describe the creation of nonclassical states of microwave radiation via ideal dichotomic single photon detection, i.e., a detector that only indicates presence or absence of photons. Ideally, such a detector has a back action in the form of the subtraction operator. Using the non-linearity of this back action, it is possible to create nonclassical states of microwave radiation, including squeezed and cat-like states, starting from a coherent state. We discuss the applicability of this protocol to current experimental designs of Josephson Photomultipliers (JPMs).   

Path Entanglement of Continuous-Variable Quantum Microwaves

Entanglement is a quantum mechanical phenomenon playing a key role in quantum communication and information processing protocols. Here, we report on frequency-degenerate entanglement between continuous-variable quantum microwaves propagating along two separated paths. In our experiment, we combine a squeezed and a vacuum state via a beam splitter. Overcoming the challenges imposed by the low photon energies in the microwave regime, we reconstruct the squeezed state and, independently from this, detect and quantify the produced entanglement via correlation measurements (E.~P.~Menzel {\it et al.}, arXiv:1210.4413). Our work paves the way towards quantum communication and teleportation with continuous variables in the microwave regime.\\ \noindent This work is supported by SFB~631, German Excellence Initiative via NIM, EU projects SOLID, CCQED and PROMISCE, MEXT Kakenhi ``Quantum Cybernetics'', JSPS FIRST Program, the NICT Commissioned Research, EPSRC EP/H050434/1, Basque Government IT472-10, and Spanish MICINN FIS2009-12773-C02-01.   

Cooper Pair Transistor Embedded in a dc-Biased High-Q Microwave Cavity

A Cooper pair transistor (CPT) is directly coupled to a high-Q microwave cavity, which allows introduction of a dc bias to the CPT without significantly degrading the cavity Q. In the subgap region of the CPT, the dc bias generates a tunable oscillating current through the CPT via the ac Josephson effect. Evidence of such self-oscillations has been observed as current peaks in our dc measurements, which are in good agreement with calculated cavity modes, and indicate the strong coupling between the CPT and the cavity. Tunneling Cooper pairs can both emit photons into and absorb photons from microwave cavity modes. Photons emitted into the cavity are also directly probed and are in good agreement with dc measurements. Recent experimental results including the importance of careful filtering of the DC bias lines will be discussed. This work is supported by the NSF, AFOSR and DARPA.   

Photon Emission from a Self-Oscillating Cavity-Embedded Cooper Pair Transistor

A strongly non-linear superconducting device consisting of a Cooper pair transistor embedded in a dc voltage biased microwave cavity is investigated. The cavity-embedded Cooper pair transistor (CCPT) is driven via the ac Josephson effect by an applied dc bias and exhibits self-oscillation without an external ac drive. Photon emission arising from both sequential tunneling and cotunnelling processes of Cooper pairs has been observed. We have characterized the measured photon field by heterodyne quadrature detection and have reconstructed its quasi-probability distribution by implementing an iterative procedure for maximum-likelihood estimation of its density matrix. The CCPT offers an interesting system for studying nonlinear quantum dynamics and the quantum-to-classical transition.   

The Quantum-Classical Correspondence for a Self-Oscillating Cavity-Embedded Cooper Pair Transistor System

We provide a theoretical model for our recent experiment involving a dc voltage biased Cooper pair transistor (CPT) that strongly drives a high quality factor microwave cavity via the ac Josephson effect. Depending on the tunable dc voltage bias, the model shows that the CPT can generate a range of non-trivial cavity quantum states involving large average microwave photon number. Using a Floquet basis approach to solving for the quantum dynamics and a Wigner function representation of the system state, we compare some of the model photon state predictions with experiment. The good agreement validates the low noise, dc biased cavity-CPT system for exploring the quantum-classical correspondence in strongly nonlinear, macroscopic systems.   

Shaping the Spontaneous Emission Pulse from a Superconducting Qubit

We report on measurements of spontaneous emission in a circuit quantum electrodynamics system. A superconducting qubit with tunable coupling to a coplanar waveguide cavity is operated in a regime where the qubit relaxation time, and consequently the spontaneous emission rate, is dominated by the interaction strength. This fast control knob on the coupling strength is used to shape the emitted single photon's wavepacket. The independent control over the coupling allows the dressed qubit frequency to remain truly constant during the emission. The wavepacket shape becomes important in experiments where quantum information needs to be transported between various nodes in a quantum network. The transfer can happen with a very high fidelity if the wavepacket is time-symmetric, since emission by the source and absorption by the destination become time reversed processes.   

Emergent Non-Adiabatic Wavefunctions for Strongly Dissipative Qubits

We show that a qubit strongly interacting with its environment leads to highly entangled states with emerging non-adiabatic features (Schrodinger-cat-like states of the environment). The model we consider is a two-level-system (qubit) coupled to a continuum of quantum oscillators (bosons), which can be realized, for instance, by a superconducting qubit coupled to a transmission line of photons. We show that the joint system is remarkably well described by a generalized variational coherent state ansatz, an ansatz which is justified by comparing with exact quantum tomography of the states found through Numerical Renormalization Group (NRG) calculations. Our coherent state ansatz includes not only the well-known polaronic contributions but also non-adiabatic anti-polaron contributions; these later contributions are critical for an accurate description of the strong coupling regime. We calculate the entanglement entropy of the qubit plus a single bosonic mode with the rest of the system; this joint entropy peaks for a bosonic mode around the Kondo scale, an effect due to the anti-polaronic contribution.   

Coherence and indistinguishability of single electron wavepackets emitted by independent sources

Using two independent on-demand electron sources [1], the emission of two single-electron wavepackets is triggered at different inputs of an electronic beamsplitter. Whereas classical particles would be randomly partitioned by the splitter, we observe two-particle interferences resulting from quantum exchange in this electronic analog [2,3] of the optical Hong-Ou-Mandel [4] experiment. Both electrons, emitted in indistinguishable wavepackets with synchronized arrival time on the splitter, exit in different outputs as recorded by the low frequency current noise. Full random partitioning is recovered when the arrival of one electron is delayed with respect to the other. This two-electron interference experiment demonstrates the possibility to generate on-demand coherent and indistinguishable single-electron wavepackets for quantum information processing in quantum conductors. [1] G. F\`{e}ve et al., Science \textbf{316}, 1169 (2007). [2] Ol'khovskaya et al., Physical Review Letters \textbf{101}, 166802 (2008). [3] T. Jonckheere et al., Phys. Rev. B \textbf{86}, 125425 (2012) [4] C. K. Hong et al., Physical Review Letters, \textbf{59}, 2044 (1987).