Observation of Berry's Phase in a Solid-State Qubit

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.When a quantum mechanical system evolves cyclically in time such that it returns to its initial physical state, its wavefunction can acquire a geometric phase factor in addition to the familiar dynamic phase [1,2]. If the cyclic change of the system is adiabatic, this additional factor is known as Berry's phase [3], and is, in contrast to dynamic phase, independent of energy and time.In quantum information science [4], a prime goal is to utilize coherent control of quantum systems to process information, accessing a regime of computation unavailable in classical systems. Quantum logic gates based on geometric phases have been demonstrated in both nuclear magnetic resonance [5] and ion trap based quantum information architectures [6]. Superconducting circuits [7,8] are a promising solid state platform for quantum information processing [9,10,11,12,13,14], in particular due to their potential scalability. Proposals for observation of geometric phase in superconducting circuits [15,16,17,18,19] have existed since shortly after the first coherent quantum effects were demonstrated in these systems [20].Geometric phases are closely linked to the classical concept of parallel transport of a vector on a curved surface. Consider, for example, a tangent vector v on the surface of a sphere being transported from the North pole around the path P shown in Fig. 1A, with v pointing South at all times. The final state of the vector v f is rotated with respect to its initial state v i by an angle φ equal to the solid angle subtended by the path P at the origin. Thus, this angle is dependent on the geometry of the path P , and is independent of the rate at which it is traversed. As a result, departures from the original path that leave the solid angle unchanged will not modify φ. This robustness has been interpreted as a potential fault tolerance when applied to quantum information processing [5].The analogy of the quantum geometric phase with the above classical picture is particularly clear in the case of a two-level system (a qubit) in the presence of a bias field that changes in time. A familiar example is a spin-1/2 particle in a changing magnetic field. The general Hamiltonian for such a system is H =hR · σ/2, where σ = (σ x , σ y , σ z ) are the Pauli operators, and R is the bias field vector, expressed in units of angular frequency. The qubit dynamics is best visualiz...

Geometric phase of the gyromotion for charged particles in a time-dependent magnetic field

“…Actually, the geometric phases in the both cases come from the same origin, the noncommutativity of the rotation operations.While the quantum geometric phases have found many important applications in optics, atomic and molecular physics, chemistry, laser physics, material science, quantum information, cosmology, etc. [25][26][27][28][29][30][31][32][33][34] , the importance and implications of the geometric phase in plasma physics are still unexplored. But we do expect interesting physics associated with the geometric phase to exist.…”

Decoherence of a solid-state qubit by different noise correlation spectra

“…Ω R /2π is the Rabi frequency. This Hamiltonian can be transformed to a rotating frame at the frequency ω by means of an unitary transformation defined by the operator U = exp (iωtσ z /2) [20] and, after the rotating wave approximation (ignoring terms oscillating at 2ω), resulting in a new effective Hamiltonian of the form…”

Pulse design without the rotating-wave approximation

“…Controlling accurately the internal states of quantum two-level systems, realized by real or artificial atoms, as in crystal defects, quantum dots, or superconducting qubits, is a fundamental task in nuclear magnetic resonance, metrology or to develop new quantum technologies [1][2][3][4][5][6][7][8][9]. Pulse engineering is the art and science of designing realizable control fields to perform specific operations.…”