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Frontiers in Optics

Synthesizing Arbitrary Photon States in a Superconducting Resonator: the Quantum Digital to Analog Converter

John M. Martinis, M. Hofheinz, H. Wang, M. Ansmann, Radoslaw C. Bialczak, Erik A. Lucero, M. Neeley, A. D. O’Connell, D. Sank, J. Wenner, Andrew N. Cleland

Published Jan 1, 2009• 0 citations

Abstract

Two-level systems, or qubits, afford complete quantum control using only classical electrical signals. Achieving the same degree of control over harmonic resonators and photons has remained elusive, due to their infinite number of equally spaced energy levels. We exploit our complete qubit control by using a superconducting phase qubit to pump microwave photons into a high-Q coplanar wave guide resonator and, subsequently, use the qubit to read out the resonator state. This scheme has previously allowed us to prepare and detect photon number states (Fock states [1]) in the resonator and to measure their decay. Using a generalization of a scheme developed by Law and Eberly [2], we can now create arbitrary quantum states of the photon field with up to approximately 10 photons [3]. We analyze the prepared states by directly mapping out the corresponding Wigner function, which is the phase-space equivalent of the density matrix, and provides a complete description of the quantum state. Movies of the decay of a variety of non-classical states show a loss of quantum coherence over the energy decay time of the resonator.

DOI: 10.1364/fio.2009.jma1

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We propose and experimentally demonstrate a new method to generate arbitrary Fock state superpositions in a superconducting quantum circuit, where a qubit is dispersively coupled to a microwave cavity mode. Here, the qubit is used to conditionally modulate the probability amplitudes of the Fock state components of a coherent state to those of the desired superposition state, instead of pumping photons one by one into the cavity as in previous schemes. Our method does not require the adjustment of the qubit frequency during the cavity state preparation and is more robust to noise and accumulation of experimental errors compared to previous ones. Using the method, we experimentally generate phase eigenstates under various Hilbert-space dimensions and squeezed states, which are useful for the quantum walk and high-precision measurement.

Quantum states inevitably decay with time into a probabilistic mixture of classical states due to their interaction with the environment and measurement instrumentation. We present the first measurement of the decoherence dynamics of complex photon states in a condensed-matter system. By controllably preparing a number of distinct quantum-superposed photon states in a superconducting microwave resonator, we show that the subsequent decay dynamics can be quantitatively described by taking into account only two distinct decay channels: energy relaxation and pure dephasing. Our ability to prepare specific initial quantum states allows us to measure the evolution of specific elements in the quantum density matrix in a very detailed manner that can be compared with theory.

We demonstrate the controlled generation of Fock states with up to 15 photons in a microwave coplanar waveguide resonator coupled to a superconducting phase qubit. The subsequent decay of the Fock states, due to dissipation, is then monitored by varying the time delay between preparing the state and performing a number-state analysis. We find that the decay dynamics can be described by a master equation where the lifetime of the n-photon Fock state scales as 1/n, in agreement with theory. We have also generated a coherent state in the microwave resonator, and monitored its decay process. We demonstrate that the coherent state maintains a Poisson distribution as it decays, with an average photon number that decreases with the same characteristic decay time as the one-photon Fock state.

Quantum entanglement, one of the defining features of quantum mechanics, has been demonstrated in a variety of nonlinear spinlike systems. Quantum entanglement in linear systems has proven significantly more challenging, as the intrinsic energy level degeneracy associated with linearity makes quantum control more difficult. Here we demonstrate the quantum entanglement of photon states in two independent linear microwave resonators, creating N-photon NOON states (entangled states |N0> + |0N>) as a benchmark demonstration. We use a superconducting quantum circuit that includes Josephson qubits to control and measure the two resonators, and we completely characterize the entangled states with bipartite Wigner tomography. These results demonstrate a significant advance in the quantum control of linear resonators in superconducting circuits.

Control electronics for superconducting quantum processors have strict requirements for accurate command of the sensitive quantum states of their qubits. Hinging on the purity of ultra-phase-stable oscillators to upconvert very-low-noise baseband pulses, conventional control systems can become prohibitively complex and expensive when scaling to larger quantum devices, especially as high sampling rates become desirable for fine-grained pulse shaping. Few-gigahertz radio-frequency (RF) digital-to-analog converters (DACs) present a more economical avenue for high-fidelity control while simultaneously providing greater command over the spectrum of the synthesized signal. Modern RF DACs with extra-wide bandwidths are able to directly synthesize tones above their sampling rates, thereby keeping the system clock rate at a level compatible with modern digital logic systems while still being able to generate high-frequency pulses with arbitrary profiles. We have incorporated custom superconducting qubit control logic into off-the-shelf hardware capable of low-noise pulse synthesis up to 7.5 GHz using an RF DAC clocked at 5 GHz. Our approach enables highly linear and stable microwave synthesis over a wide bandwidth, giving rise to high-resolution control and a reduced number of required signal sources per qubit. We characterize the performance of the hardware using a five-transmon superconducting device and demonstrate consistently reduced two-qubit gate error (as low as 1.8%), which we show results from superior control chain linearity compared to traditional configurations. The exceptional flexibility and stability further establish a foundation for scalable quantum control beyond intermediate-scale devices.