Physical Review A

Coherent and optimal control of adiabatic motion of ions in a trap

Meiyu Zhao, Dmitri Babikov

Published Jan 31, 2008• 18 citations

Abstract

Small anharmonicity, created along the axial direction of the trap, allows controlling the motional states of ions adiabatically using electric fields. In this paper several important aspects of this control scheme are explored theoretically. The pulses for various state transformations, including universal quantum gates, are derived using the optimal control theory. They exhibit simple shapes and other favorable properties, which indicate a promising route for practical implementation.

DOI: 10.1103/physreva.77.012338

Related papers

Adiabatic coherent control in the anharmonic ion trap: Proposal for the vibrational two-qubit system

Lei Wang, Dmitri Babikov

A method for encoding a multiqubit system into the quantized motional states of ion string in an anharmonic linear trap is proposed. Control over this system is achieved by applying oscillatory electric fields (rf) shaped optimally for desired state-to-state transitions. Anharmonicity of the vibrational spectrum of the system plays a key role in this approach to the control and quantum computation, since it allows resolving different state-to-state transitions and addressing them selectively. The anharmonic trap architecture proposed earlier [Phys. Rev. A 83, 022305 (2011)] is explored here and the optimal control theory is used to derive pulses for a set of universal quantum gates. An accurate choice of pulse parameters allows deriving gates that are both accurate and simple. A practical realization of this approach seems to be within the reach of today's technology.

Physical Review AMay 20, 20116 citations

Adiabatic coherent control in the anharmonic ion trap: Numerical analysis of vibrational anharmonicities

Lei Wang, Dmitri Babikov

Anharmonicity of the quantized motional states of ions in a Paul trap can be utilized to address the state-to-state transitions selectively and control the motional modes of trapped ions coherently and adiabatically [Zhao and Babikov, Phys. Rev. A 77, 012338 (2008)]. In this paper we study two sources of the vibrational anharmonicity in the ion traps: the intrinsic Coulomb anharmonicity due to ion-ion interactions and the external anharmonicity of the trapping potential. An accurate numerical approach is used to compute energies and wave functions of vibrational eigenstates. The magnitude of the Coulomb anharmonicity is determined and shown to be insufficient for successful control. In contrast, anharmonicity of the trapping potential allows one to control the motion of ions very efficiently using the time-varying electric fields. Optimal control theory is used to derive the control pulses. One ion in a slightly anharmonic trap can be easily controlled. In the two- and three-ion systems the symmetric stretching mode is dark and cannot be controlled at all. The other two normal modes of the three-ion system can be controlled and used, for example, to encode a two-qubit system into the motional states of ions. A trap architecture that allows the necessary amount of vibrational anharmonicity to be achieved is proposed.

Physical Review AFeb 7, 201112 citations

Computational study of vibrational qubits in anharmonic linear ion traps

Lei Wang

A string of cold ions confined in a linear trap represents a man-made quantum object with a broad range of applications in atomic and molecular spectroscopy, such as high-precision measurement of atomic properties. An efficient isolation from the environment guarantees excellent coherent properties of such systems and makes them suitable for practical realization of the quantum information processing. The pioneering theoretical [Cirac and Zoller] and experimental [Wineland and Monroe] work in 1990s resulted in the explosive expansion of this field during the last decade. In this dissertation an alternative new method for controlling the quantized motional/vibrational states of ions in a trap is explored theoretically. It is proposed to create small anharmonicity in the trapping potential which would modify the spectrum of states and allow addressing the state-to-state transitions selectively. In this approach all ions remain in the ground electronic state and their motion is controlled adiabatically and coherently by applying the optimally shaped electric fields (RF). The optimal control theory, accurate numerical calculation of the energies and wavefunctions, and numerical propagation of wave packets are employed. Two sources of vibrational anharmonicity are studied: the intrinsic Coulomb anharmonicity due to the ion-ion interactions and the external anharmonicity of the trapping potential. It is shown that the magnitude of Coulomb anharmonicity is insufficient for the control. In contrast, anharmonicity of the trapping potential allows controlling the motion of ions very accurately. It is demonstrated that one ion in a slightly anharmonic trap can be easily controlled and used to represent one qubit. A multi-qubit system can be created by employing a long progression of states of a single ion, or by trapping multiple ions and controlling several normal vibration modes of the ion string. Up to four qubits are modeled in this work and accurate pulses are optimized for a set of universal quantum gates: NOT, conditional NOT (CNOT) and Hadamard transformation. The control field for Shor's algorithm (quantum algorithm for factorization onto prime numbers) is also obtained. It is demonstrated that a careful choice of system properties allows achieving very high accuracy of qubit transformations, up to 0.999.

Jan 1, 20120 citations

Feasibility of encoding Shor's algorithm into the motional states of an ion in the anharmonic trap

Lei Wang, Dmitri Babikov

We demonstrate theoretically that it may be possible to encode states of a multi-qubit system into the progression of quantized motional∕vibrational levels of an ion trapped in a weakly anharmonic potential. Control over such register of quantum information is achieved by applying oscillatory radio-frequency fields shaped optimally for excitation of the desired state-to-state transitions. Anharmonicity of the vibrational spectrum plays a key role in this approach to the control and quantum computation, since it allows resolving different state-to-state transitions and addressing them selectively. Optimal control theory is used to derive pulses for implementing the four-qubit version of Shor's algorithm in a single step. Accuracy of the qubit-state transformations, reached in the numerical simulations, is around 0.999. Very detailed insight is obtained by analysis of the time-evolution of state populations and by spectral analysis of the optimized pulse.

The Journal of Chemical PhysicsAug 8, 20126 citations

Directional motional control via engineered conical intersections in trapped Rydberg ions

Abdessamad Belfakir, Yousra Bouasria, HERSCHEL A. RABITZ +1 more

We demonstrate coherent control of motional dynamics in trapped Rydberg ions engineered to exhibit a conical intersection between adiabatic potential-energy surfaces. Using quantum optimal control, an optimally shaped electric field drives the motional wave packet between prescribed spatial configurations on microsecond timescales. Localized nonadiabatic coupling breaks the symmetry of the dynamics and produces a directed trajectory: after only a few early passages through the conical intersection region, the packet proceeds toward the target with high fidelity. In contrast, in the Born-Oppenheimer limit, where such coupling is absent, the optimized control yields symmetric, multicycle oscillations rather than a comparably directed displacement. While both approaches reach the target at the chosen final time, the underlying trajectories are qualitatively different. This work demonstrates that engineered conical intersections can serve as a potential control resource for directional motional dynamics, complementing pulse-shaping methods in trapped-ion systems. This directional motion of the ions, enabled by the conical intersection, may provide a route toward improved control of motional states in trapped-ion quantum information processing.

arXiv:2509.11350Physical Review AMay 1, 20260 citations

Coherently manipulating cold ions in separated traps by their vibrational couplings II: non-adiabatic case

Miao Zhang, L. F. Wei

An approach is proposed to implement the universal quantum gates between the ions confined individually in the separated traps. Instead of the typical adiabatic operations, performed for manipulating the ion-ion coupling, here the switchable couplings between ions are implemented non-adiabatically by using the fast laser pulses. Consequently, the desirable quantum gates between the ions could be implemented by using only a series of laser pulses. The proposal may be conveniently generalized to the quantum computation with the scalable ion-traps.

Jul 25, 20110 citations