Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0902.4271 · American Journal of Physics

Double well potentials and quantum gates

Christopher J. Foot, Martin Shotter

Published Jun 17, 2011• 22 citations
arXivHTMLPDF

Abstract

A system of particles in a double well potential is a widely studied and useful example for understanding quantum mechanics. This simple system has recently been used in theoretical proposals and related experiments as a way to make quantum logic gates for ultracold atoms confined in optical lattices. Such quantum gates are the fundamental building blocks for quantum information processing; in these proposals, a regular array of cold atoms in an optical lattice serves as the quantum register. We explain how this research can be understood in terms of well-known principles for systems of identical particles.

DOI
10.1119/1.3583478

Related papers

Entanglement with quantum gates in an optical lattice

Olaf Mandel

The concept of a "quantum computer" has attracted much attention in recent years. Many research groups around the world are studying the extraordinary potential of quantum computers and attempting their realisation. Current fundamental experiments are directed towards the individual building blocks of such a computer. The concept of using quantum mechanical systems to calculate complex problems was created in 1982 with Feynmans proposal of the quantum simulator. This concept represents a well controlled framework of interacting quantum systems. The intention is to map a different system of interest not mastered in the lab onto the quantum simulator. From the behaviour of the quantum simulator the behaviour of the system of interest can be deduced. A quantum mechanical measurement on the quantum simulator is thus comparable to one run of a numerical simulation of the system of interest. The difference is that a numerical simulation can often only be run under severe simplifications that then challenge the practical relevance of the result. Only very small quantum systems can be calculated on today's computers without simplifications. In this work a system of ground state atoms stored in a 3D optical lattice is presented. Each of the up to 100,000 atoms is stored in its own potential minimum, isolated from the other atoms. This state is a formidable starting point for the realisation of a quantum simulator: every atom is considered the information carrier of a spin-1/2 system. Only very few of the other concepts currently under investigation have as many information carriers as a Mott-Insulator state in an optical lattice. We have already shown in preparatory experiments a long storage time and good coherence times. Here this system is extended by a major prerequisite for a quantum simulator: controllable interactions between individual atoms are essential in order to model the interaction terms of the system of interest. These interactions are realised by a state-selective in the optical lattice by state-selective trapping potentials. If the states of an atom are called |0> and |1>, then there are two distinct potentials V0 and V1 that each act on only one of the states. The two potentials are shifted with respect to each other and thus allow bringing neighbouring atoms into contact. Since the shifting is always performed along one of the three lattice axes, the interaction is not confined to a single pair of atoms, but all pairs of neighbouring atoms along a lattice axis interact. This inherent parallelism has allowed us to create entanglement in large systems in just a single operation. The entanglement has then been measured in a Ramsey interferometer. A sequence of one nearest-neighbour interaction produces the cluster state, a maximally entangled state. More recent proposals suggest to use a cluster state as the basis for a new kind of quantum computer. As opposed to today's computers, this quantum computer would not be a Touring machine whose working algorithm is only controlled by programming. Instead the wiring of the quantum gates would have to be changed in order to solve a new problem. This is loosely comparable to today's FPGA (Field Programmable Gate Arrays - programmable logic chips). Until these quantum computers are built, quite some improvements on the experimental techniques will be necessary. But the first quantum simulators are now practically within reach.

•Jan 1, 2005•3 citations

Cold bosons in optical lattices

Vyacheslav I. Yukalov

Basic properties of cold Bose atoms in optical lattices are reviewed. The main principles of correct self-consistent description of arbitrary systems with Bose-Einstein condensate are formulated. Theoretical methods for describing regular periodic lattices are presented. A special attention is paid to the discussion of Bose-atom properties in the frame of the boson Hubbard model. Optical lattices with arbitrary strong disorder, induced by random potentials, are treated. Possible applications of cold atoms in optical lattices are discussed, with an emphasis of their usefulness for quantum information processing and quantum computing. An important feature of the present review article, distinguishing it from other review works, is that theoretical fundamentals here are not just mentioned in brief, but are thoroughly explained. This makes it easy for the reader to follow the principal points without the immediate necessity of resorting to numerous publications in the field.

arXiv:0901.0636•Laser Physics•Jan 1, 2009•208 citations

Quantum control and information processing in optical lattices

Poul Jessen, D. L. Haycock, Gerd Klose +3 more

Neutral atoms offer a promising platform for single- and many-body quantum control, as required for quantum information processing. This includes excellent isolation from the decohering influence of the environment, and the existence of well developed techniques for atom trapping and coherent manipulation. We present a review of our work to implement quantum control and measurement for ultra-cold atoms in far-off-resonance optical lattice traps. In recent experiments we have demonstrated coherent behavior of mesoscopic atomic spinor wavepackets in optical double-well potentials, and carried out quantum state tomography to reconstruct the full density matrix for the atomic spin degrees of freedom. This model system shares a number of important features with proposals to implement quantum logic and quantum computing in optical lattices. We present a theoretical analysis of a protocol for universal quantum logic via single qubit operations and an entangling gate based on electric dipole-dipole interactions. Detailed calculations including the full atomic hyperfine structure suggests that high-fidelity quantum gates are possible under realistic experimental conditions.

Quantum Information and Computation•Dec 1, 2001•13 citations

Quantum Information Processing on the Basis of Single Ultracold Atoms in Optical Traps

I. I. Ryabtsev, K. Yu. Mityanin, Ilya I. Beterov +5 more

Abstract A brief overview of experimental and theoretical studies on the use of single neutral atoms captured in arrays of optical dipole traps as qubits of a quantum computer is presented. Methods for loading and registering atoms in traps, and performing two-qubit quantum logic gates via dipole-dipole interaction during short-term laser excitation of atoms into Rydberg states are discussed.

Optoelectronics Instrumentation and Data Processing•Sep 1, 2020•2 citations

Conditional Quantum Dynamics and Logic Gates

Adriano Barenco, David Deutsch, ARTUR K. EKERT +1 more

Quantum logic gates provide fundamental examples of conditional quantum dynamics. They could form the building blocks of general quantum information processing systems which have recently been shown to have many interesting nonclassical properties. We describe a simple quantum logic gate, the quantum controlled-NOT, and analyze some of its applications. We discuss two possible physical realizations of the gate, one based on Ramsey atomic interferometry and the other on the selective driving of optical resonances of two subsystems undergoing a dipole-dipole interaction.

arXiv:quant-ph/9503017•Physical Review Letters•May 15, 1995•969 citations

Double well potentials for atomic qubit gates in a designer optical lattice

J. H. Huckans, Chad Fertig, Ian B. Spielman +2 more

Using four coherent laser beams we make two different 2D optical lattices with polarization-dependent periodicity. The lattices are coincident, and by shifting one with respect to the other, we create an array of double well potentials. We have designed a 2D optical lattice for /sup 87/Rb atoms consisting of an array of double well potentials. This lattice should allow us to test two-qubit gates and in general permit atomic control in support of nearest neighbor interaction physics such as the Ising model and quantum cellular automata.

Quantum Electronics and Laser Science Conference•Dec 10, 2005•0 citations
A system of particles in a double well potential is a widely studied and useful example for understanding quantum mechanics. This simple system has recently been used in theoretical proposals and related experiments as a way to make quantum logic gates for ultracold atoms confined in optical lattices. Such quantum gates are the fundamental building blocks for quantum information processing; in these proposals, a regular array of cold atoms in an optical lattice serves as the quantum register. We explain how this research can be understood in terms of well-known principles for systems of identical particles.
The concept of a "quantum computer" has attracted much attention in recent years. Many research groups around the world are studying the extraordinary potential of quantum computers and attempting their realisation. Current fundamental experiments are directed towards the individual building blocks of such a computer. The concept of using quantum mechanical systems to calculate complex problems was created in 1982 with Feynmans proposal of the quantum simulator. This concept represents a well controlled framework of interacting quantum systems. The intention is to map a different system of interest not mastered in the lab onto the quantum simulator. From the behaviour of the quantum simulator the behaviour of the system of interest can be deduced. A quantum mechanical measurement on the quantum simulator is thus comparable to one run of a numerical simulation of the system of interest. The difference is that a numerical simulation can often only be run under severe simplifications that then challenge the practical relevance of the result. Only very small quantum systems can be calculated on today's computers without simplifications. In this work a system of ground state atoms stored in a 3D optical lattice is presented. Each of the up to 100,000 atoms is stored in its own potential minimum, isolated from the other atoms. This state is a formidable starting point for the realisation of a quantum simulator: every atom is considered the information carrier of a spin-1/2 system. Only very few of the other concepts currently under investigation have as many information carriers as a Mott-Insulator state in an optical lattice. We have already shown in preparatory experiments a long storage time and good coherence times. Here this system is extended by a major prerequisite for a quantum simulator: controllable interactions between individual atoms are essential in order to model the interaction terms of the system of interest. These interactions are realised by a state-selective in the optical lattice by state-selective trapping potentials. If the states of an atom are called |0> and |1>, then there are two distinct potentials V0 and V1 that each act on only one of the states. The two potentials are shifted with respect to each other and thus allow bringing neighbouring atoms into contact. Since the shifting is always performed along one of the three lattice axes, the interaction is not confined to a single pair of atoms, but all pairs of neighbouring atoms along a lattice axis interact. This inherent parallelism has allowed us to create entanglement in large systems in just a single operation. The entanglement has then been measured in a Ramsey interferometer. A sequence of one nearest-neighbour interaction produces the cluster state, a maximally entangled state. More recent proposals suggest to use a cluster state as the basis for a new kind of quantum computer. As opposed to today's computers, this quantum computer would not be a Touring machine whose working algorithm is only controlled by programming. Instead the wiring of the quantum gates would have to be changed in order to solve a new problem. This is loosely comparable to today's FPGA (Field Programmable Gate Arrays - programmable logic chips). Until these quantum computers are built, quite some improvements on the experimental techniques will be necessary. But the first quantum simulators are now practically within reach.
Basic properties of cold Bose atoms in optical lattices are reviewed. The main principles of correct self-consistent description of arbitrary systems with Bose-Einstein condensate are formulated. Theoretical methods for describing regular periodic lattices are presented. A special attention is paid to the discussion of Bose-atom properties in the frame of the boson Hubbard model. Optical lattices with arbitrary strong disorder, induced by random potentials, are treated. Possible applications of cold atoms in optical lattices are discussed, with an emphasis of their usefulness for quantum information processing and quantum computing. An important feature of the present review article, distinguishing it from other review works, is that theoretical fundamentals here are not just mentioned in brief, but are thoroughly explained. This makes it easy for the reader to follow the principal points without the immediate necessity of resorting to numerous publications in the field.
Neutral atoms offer a promising platform for single- and many-body quantum control, as required for quantum information processing. This includes excellent isolation from the decohering influence of the environment, and the existence of well developed techniques for atom trapping and coherent manipulation. We present a review of our work to implement quantum control and measurement for ultra-cold atoms in far-off-resonance optical lattice traps. In recent experiments we have demonstrated coherent behavior of mesoscopic atomic spinor wavepackets in optical double-well potentials, and carried out quantum state tomography to reconstruct the full density matrix for the atomic spin degrees of freedom. This model system shares a number of important features with proposals to implement quantum logic and quantum computing in optical lattices. We present a theoretical analysis of a protocol for universal quantum logic via single qubit operations and an entangling gate based on electric dipole-dipole interactions. Detailed calculations including the full atomic hyperfine structure suggests that high-fidelity quantum gates are possible under realistic experimental conditions.
Quantum logic gates provide fundamental examples of conditional quantum dynamics. They could form the building blocks of general quantum information processing systems which have recently been shown to have many interesting nonclassical properties. We describe a simple quantum logic gate, the quantum controlled-NOT, and analyze some of its applications. We discuss two possible physical realizations of the gate, one based on Ramsey atomic interferometry and the other on the selective driving of optical resonances of two subsystems undergoing a dipole-dipole interaction.
Using four coherent laser beams we make two different 2D optical lattices with polarization-dependent periodicity. The lattices are coincident, and by shifting one with respect to the other, we create an array of double well potentials. We have designed a 2D optical lattice for /sup 87/Rb atoms consisting of an array of double well potentials. This lattice should allow us to test two-qubit gates and in general permit atomic control in support of nearest neighbor interaction physics such as the Ising model and quantum cellular automata.