Revealing hidden quantum correlations in an electromechanical measurement

  1. C. F. Ockeloen-Korppi,
  2. E. Damskägg,
  3. G. S. Paraoanu,
  4. F. Massel,
  5. and M. A. Sillanpää
Under a strong quantum measurement, the motion of an oscillator is disturbed by the measurement back-action, as required by the Heisenberg uncertainty principle. When a mechanical oscillator
is continuously monitored via an electromagnetic cavity, as in a cavity optomechanical measurement, the back-action is manifest by the shot noise of incoming photons that becomes imprinted onto the motion of the oscillator. Following the photons leaving the cavity, the correlations appear as squeezing of quantum noise in the emitted field. Here we observe such „ponderomotive“ squeezing in the microwave domain using an electromechanical device made out of a superconducting resonator and a drumhead mechanical oscillator. Under a strong measurement, the emitted field develops complex-valued quantum correlations, which in general are not completely accessible by standard homodyne measurements. We recover these hidden correlations, using a phase-sensitive measurement scheme employing two local oscillators. The utilization of hidden correlations presents a step forward in the detection of weak forces, as it allows to fully utilize the quantum noise reduction under the conditions of strong force sensitivity.

Experimental state control by fast non-Abelian holonomic gates with a superconducting qutrit

  1. S. Danilin,
  2. A. Vepsäläinen,
  3. and G. S. Paraoanu
Quantum state manipulation with gates based on geometric phases acquired during cyclic operations promises inherent fault-tolerance and resilience to local fluctuations in the control
parameters. Here we create a general non-Abelian and non-adiabatic holonomic gate acting in the $(\ket{0},\ket{2})$ subspace of a three-level transmon fabricated in a fully coplanar design. Experimentally, this is realized by simultaneously coupling the first two transitions by microwave pulses with amplitudes and phases defined such that the condition of parallel transport is fulfilled. We demonstrate the creation of arbitrary superpositions in this subspace by changing the amplitudes of the pulses and the relative phase between them. We use two-photon pulses acting in the holonomic subspace to reveal the coherence of the state created by the geometric gate pulses and to prepare different superposition states. We also test the action of holonomic NOT and Hadamard gates on superpositions in the $(\ket{0},\ket{2})$ subspace.

Quantum-enhanced magnetometry by phase estimation algorithms with a single artificial atom

  1. S. Danilin,
  2. A. V. Lebedev,
  3. A. Vepsäläinen,
  4. G. B. Lesovik,
  5. G. Blatter,
  6. and G. S. Paraoanu
Phase estimation algorithms are key protocols in quantum information processing. Besides applications in quantum computing, they can also be employed in metrology as they allow for
fast extraction of information stored in the quantum state of a system. Here, we implement two suitably modified phase estimation procedures, the Kitaev- and the semiclassical Fourier-transform algorithms, using an artificial atom realized with a superconducting transmon circuit. We demonstrate that both algorithms yield a flux sensitivity exceeding the classical shot-noise limit of the device, allowing one to approach the Heisenberg limit. Our experiment paves the way for the use of superconducting qubits as metrological devices which are potentially able to outperform the best existing flux sensors with a sensitivity enhanced by few orders of magnitude.

Quantum metrology with a transmon qutrit

  1. A. R. Shlyakhov,
  2. V. V. Zemlyanov,
  3. M. V. Suslov,
  4. A. V. Lebedev,
  5. G. S. Paraoanu,
  6. G. B. Lesovik,
  7. and G. Blatter
Making use of coherence and entanglement as metrological quantum resources allows to improve the measurement precision from the shot-noise- or quantum limit to the Heisenberg limit.
Quantum metrology then relies on the availability of quantum engineered systems that involve controllable quantum degrees of freedom which are sensitive to the measured quantity. Sensors operating in the qubit mode and exploiting their coherence in a phase-sensitive measurement have been shown to approach the Heisenberg scaling in precision. Here, we show that this result can be further improved by operating the quantum sensor in the qudit mode, i.e., by exploiting d rather than 2 levels. Specifically, we describe the metrological algorithm for using a superconducting transmon device operating in a qutrit mode as a magnetometer. The algorithm is based on the base-3 semi-quantum Fourier transformation and enhances the quantum theoretical performance of the sensor by a factor 2. Even more, the practical gain of our qutrit-implementation is found in a reduction of the number of iteration steps of the quantum Fourier transformation by a factor log2/log3≈0.63 as compared to the qubit mode. We show, that a two-tone capacitively coupled rf-signal is sufficient for the implementation of the algorithm.

Cross-coupling effects in circuit-QED stimulated Raman adiabatic passage

  1. A. Vepsäläinen,
  2. and G. S. Paraoanu
Stimulated Raman adiabatic passage is a quantum protocol that can be used for robust state preparation in a three-level system. It has been commonly employed in quantum optics, but
recently this technique has drawn attention also in circuit quantum electrodynamics. The protocol relies on two slowly varying drive pulses that couple the initial and the target state via an intermediate state, which remains unpopulated. Here we study the detrimental effect of the parasitic couplings of the drives into transitions other than those required by the protocol. The effect is most prominent in systems with almost harmonic energy level structure, such as the transmon. We show that under these conditions in the presence of decoherence there exists an optimal STIRAP amplitude for population transfer.

Advances in quantum control of three-level superconducting circuit architectures

  1. G. Falci,
  2. P. G. Di Stefano,
  3. A. Ridolfo,
  4. A. D'Arrigo,
  5. G. S. Paraoanu,
  6. and E. Paladino
Advanced control in Lambda (Λ) scheme of a solid state architecture of artificial atoms and quantized modes would allow the translation to the solid-state realm of a whole class of
phenomena from quantum optics, thus exploiting new physics emerging in larger integrated quantum networks and for stronger couplings. However control solid-state devices has constraints coming from selection rules, due to symmetries which on the other hand yield protection from decoherence, and from design issues, for instance that coupling to microwave cavities is not directly switchable. We present two new schemes for the Λ-STIRAP control problem with the constraint of one or two classical driving fields being always-on. We show how these protocols are converted to apply to circuit-QED architectures. We finally illustrate an application to coherent spectroscopy of the so called ultrastrong atom-cavity coupling regime.

Observation of the Bloch-Siegert shift in the driven quantum-to-classical transition of a dispersive transmon qubit

  1. I. Pietikäinen,
  2. S. Danilin,
  3. K. S. Kumar,
  4. D. S. Golubev,
  5. J. Tuorila,
  6. and G. S. Paraoanu
We demonstrate the Bloch-Siegert effect in a dispersively coupled qubit-cavity system which is driven through a quantum-to-classical transition. The observed dispersive shift of the
resonance frequency displays strongly non-monotonic dependence on the number of cavity photons and escapes the scope of the analytic results obtained with either a simple rotating-wave approximation, or with a more refined counter-rotating hybridized rotating wave approach. We measured the transition energy with a weak resonant probe, and the obtained data is in a good agreement with our numerical simulations of the quasienergy spectrum.

Coherence from vacuum fluctuations

  1. Pasi Lähteenmäki,
  2. G. S. Paraoanu,
  3. Juha Hassel,
  4. and Pertti Hakonen
The existence of vacuum fluctuations is one of the most important predictions of modern quantum field theory. In the vacuum state, fluctuations occurring at different frequencies are
uncorrelated. However, if a parameter in the Lagrangian of the field is modulated by an external pump, vacuum fluctuations stimulate spontaneous downconversion processes, creating squeezing between modes symmetric with respect to half of the frequency of the pump. Here we show that by double parametric pumping of a superconducting microwave cavity in the ground state, it is possible to generate another fundamental type of correlation, namely coherence between photons in separate frequency modes that are not directly connected through a single downconversion process. The coherence is tunable by the phases of the pumps and it is established by a quantum fluctuation that takes simultaneously part in creation of two photon pairs. Our analysis indicates that the origin of this vacuum-induced coherence is the absence of „which-way“ information in the frequency space.

Stimulated Raman adiabatic passage in a three-level superconducting circuit

  1. K. S. Kumar,
  2. A. Vepsalainen,
  3. S. Danilin,
  4. and G. S. Paraoanu
The adiabatic manipulation of quantum states is a powerful technique that has opened up new directions in quantum engineering, enabling tests of fundamental concepts such as the Berry
phase and its nonabelian generalization, the observation of topological transitions, and holds the promise of alternative models of quantum computation. Here we benchmark the stimulated Raman adiabatic passage process for circuit quantum electrodynamics, by using the first three levels of a transmon qubit. We demonstrate a population transfer efficiency above 80% between the ground state and the second excited state using two adiabatic Gaussian-shaped control microwave pulses coupled to the first and second transition. The advantage of this techniques is robustness against errors in the timing of the control pulses. By doing quantum tomography at successive moments during the Raman pulses, we investigate the transfer of the population in time-domain. We also show that this protocol can be reversed by applying a third adiabatic pulse on the first transition. Furthermore, we demonstrate a hybrid adiabatic-nonadiabatic gate using a fast pulse followed by the adiabatic Raman sequence, and we study experimentally the case of a quasi-degenerate intermediate level.

Stückelberg interference in a superconducting qubit under periodic latching modulation

  1. M. P. Silveri,
  2. K. S. Kumar,
  3. J. Tuorila,
  4. J. Li,
  5. A. Vepsäläinen,
  6. E. V. Thuneberg,
  7. and G. S. Paraoanu
When the transition frequency of a qubit is modulated periodically across an avoided crossing along its energy dispersion curve, tunnelling to the excited state – and consequently
Landau-Zener-St\“uckelberg interference – can occur. The types of modulation studied so far correspond to a continuous evolution of the system along the dispersion curve. Here we introduce a type of modulation called periodic latching, in which the qubit’s free phase evolution is interrupted by sudden switches in the transition frequency. In this case, the conventional Landau-Zener-St\“uckelberg theory becomes inadequate and we develop a novel adiabatic-impulse model for the evolution of the system. We derive the resonance conditions and we identify two regimes: a slow-modulation regime and a fast-modulation regime, in which case the rotating wave approximation (RWA) can be applied to obtain analytical results. The adiabatic-impulse model and the RWA results are compared with those of a full numerical simulation. These theoretical predictions are tested in an experimental setup consisting of a transmon whose flux bias is modulated with a square wave form. A rich spectrum with distinctive features in the slow-modulation and fast-modulation (RWA) regimes is observed and shown to be in very good agreement with the theoretical models. Also, differences with respect to the well known case of sinusoidal modulation are discussed, both theoretically and experimentally.