Observation of Berry's Phase in a Solid State Qubit (0711.0218v1)

Abstract: In quantum information science, the phase of a wavefunction plays an important role in encoding information. While most experiments in this field rely on dynamic effects to manipulate this information, an alternative approach is to use geometric phase, which has been argued to have potential fault tolerance. We demonstrate the controlled accumulation of a geometric phase, Berry's phase, in a superconducting qubit, manipulating the qubit geometrically using microwave radiation, and observing the accumulated phase in an interference experiment. We find excellent agreement with Berry's predictions, and also observe a geometry dependent contribution to dephasing.

• The paper demonstrates the reliable measurement of Berry's phase in a superconducting qubit using Ramsey interference techniques.
• It employs a circuit QED setup with microwave modulation, achieving energy relaxation and coherence times of approximately 10 µs and 2 µs, respectively.
• The findings validate the use of geometric phase for fault-tolerant quantum operations, despite challenges from low-frequency geometric dephasing.

Observation of Berry's Phase in a Solid State Qubit

The paper "Observation of Berry's Phase in a Solid State Qubit" presents an important experimental observation of Berry's phase in a superconducting qubit system. This paper is conducted within the context of quantum information science, where the geometric phase offers potential advantages in fault-tolerant quantum computation due to its robustness against certain types of noise.

Experimental Overview

The authors employ a superconducting Cooper pair box qubit, which is embedded in a one-dimensional microwave transmission line resonator. This setup is part of the circuit quantum electrodynamics (circuit QED) architecture. The qubit is driven by microwave radiation, allowing for precise control of the geometric phase accumulated during the evolution of the qubit system. The experiment effectively demonstrates that Berry's phase can be evaluated using interference experiments based on the Ramsey fringe protocol. The authors find the measured accumulated phase to be in excellent agreement with theoretical predictions, confirming the viability of utilizing geometric phases in solid-state quantum computing.

Technical Observations

1. Qubit Implementation and Control: The superconducting qubit, realized as a Cooper pair box, is highly isolated from environmental noise due to the circuit QED architecture. Phase and amplitude modulation of the microwave field controls the qubit, enabling the desired dynamic and geometric paths in the Hilbert space. The paper declares an impressive energy relaxation time of approximately $T_1 \approx 10 \mu s$ and a spin-echo coherence time of $T_2^{\rm echo} \approx 2 \mu s$.
2. Geometric Phase Accumulation: The protocol involves a controlled accumulation of geometric phase by manipulating the path of the effective magnetic field vector. During cyclic adiabatic evolution, the qubit states traverse closed paths in the parameter space of the Hamiltonian, allowing for the measurement of Berry's phase through qubit state tomography.
3. Phase Measurement: The researchers quantify Berry's phase through repeated Ramsey interference experiments. Geometric dephasing, linked to low-frequency fluctuations, is noted as a significant feature of such geometric manipulations, contrasting with the anticipated noise resilience provided against high-frequency variations.

Results and Implications

The experimental results robustly demonstrate that Berry's phase can be reliably controlled and measured in a superconducting qubit. The dependence of dephasing on the geometry of the path traversed points to important practical considerations for utilizing geometric phases in quantum computation. Particularly noteworthy is the distinction between geometric dephasing due to low-frequency noise and the inherent fault tolerance to high-frequency noise, emphasizing Berry's phase's potential in developing fault-tolerant quantum gates.

Future Directions

Further research could explore scaling such experiments to more complex qubit systems and integrating geometric phases into larger quantum circuits. As superconducting qubits move towards practical quantum computing applications, understanding and mitigating geometric dephasing effects while leveraging the robustness against high-frequency noise could prove beneficial. Research could also target optimizing adiabatic control methods or exploring Berry's phase in other quantum systems to elucidate the universality of these concepts in quantum information processing.

The findings of this paper exemplify the ongoing progress in embedding geometric phase concepts into quantum computation frameworks, providing insights critical for the advancement of robust quantum technologies.