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Physical Review A

Generating and controlling chains of entangled atoms by coherent control techniques

Moshe Shapiro

Published Nov 28, 2011• 6 citations
Publisher

Abstract

A practical way of writing long sequences of entangled atomic qubits using coherent control with classical light sources is proposed. The method utilizes one-photon vs two-photon interference as a means of controlling the directionality of the motion of valence electrons during molecular dissociation processes. We show that, by dissociating in an optical lattice a one-dimensional array of ultracold diatomic molecules (e.g., ${\mathrm{Na}}_{2}\ensuremath{\rightarrow}\mathrm{Na}+{\mathrm{Na}}^{*}$), using a combination of photoabsorption of two mutually perpendicularly polarized beams at center frequency $\ensuremath{\omega}$ and a coherent Raman transition at frequencies ${\ensuremath{\omega}}_{1}$ and ${\ensuremath{\omega}}_{2}={\ensuremath{\omega}}_{1}\ensuremath{-}\ensuremath{\omega}$, one can craft entangled states composed of arbitrary superpositions of sequences of atomic states, such as $|f\ensuremath{\rangle}|f\ensuremath{\rangle}|b\ensuremath{\rangle}+\ensuremath{\cdots}+|b\ensuremath{\rangle}|b\ensuremath{\rangle}|f\ensuremath{\rangle}+\ensuremath{\cdots},$ where $|f\ensuremath{\rangle}$ designates a dissociation process in which the ground-state Na atom goes in the forwarddirection and the excited-state Na${}^{*}$ goes in the backward direction, while $|b\ensuremath{\rangle}$ designates the reverse process, namely, Na going in the backward direction and Na${}^{*}$ going in the forward direction. The method, which on the basis of past work is expected to be robust against decoherence, would enable the encoding of very long sequences of entangled qubits.

DOI
10.1103/physreva.84.053432

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A practical way of writing long sequences of entangled atomic qubits using coherent control with classical light sources is proposed. The method utilizes one-photon vs two-photon interference as a means of controlling the directionality of the motion of valence electrons during molecular dissociation processes. We show that, by dissociating in an optical lattice a one-dimensional array of ultracold diatomic molecules (e.g., Na2\ensuremath→Na+Na∗{\mathrm{Na}}_{2}\ensuremath{\rightarrow}\mathrm{Na}+{\mathrm{Na}}^{*}Na2​\ensuremath→Na+Na∗), using a combination of photoabsorption of two mutually perpendicularly polarized beams at center frequency \ensuremathω\ensuremath{\omega}\ensuremathω and a coherent Raman transition at frequencies \ensuremathω1{\ensuremath{\omega}}_{1}\ensuremathω1​ and \ensuremathω2=\ensuremathω1\ensuremath−\ensuremathω{\ensuremath{\omega}}_{2}={\ensuremath{\omega}}_{1}\ensuremath{-}\ensuremath{\omega}\ensuremathω2​=\ensuremathω1​\ensuremath−\ensuremathω, one can craft entangled states composed of arbitrary superpositions of sequences of atomic states, such as ∣f\ensuremath⟩∣f\ensuremath⟩∣b\ensuremath⟩+\ensuremath⋯+∣b\ensuremath⟩∣b\ensuremath⟩∣f\ensuremath⟩+\ensuremath⋯,|f\ensuremath{\rangle}|f\ensuremath{\rangle}|b\ensuremath{\rangle}+\ensuremath{\cdots}+|b\ensuremath{\rangle}|b\ensuremath{\rangle}|f\ensuremath{\rangle}+\ensuremath{\cdots},∣f\ensuremath⟩∣f\ensuremath⟩∣b\ensuremath⟩+\ensuremath⋯+∣b\ensuremath⟩∣b\ensuremath⟩∣f\ensuremath⟩+\ensuremath⋯, where ∣f\ensuremath⟩|f\ensuremath{\rangle}∣f\ensuremath⟩ designates a dissociation process in which the ground-state Na atom goes in the forwarddirection and the excited-state Na∗{}^{*}∗ goes in the backward direction, while ∣b\ensuremath⟩|b\ensuremath{\rangle}∣b\ensuremath⟩ designates the reverse process, namely, Na going in the backward direction and Na∗{}^{*}∗ going in the forward direction. The method, which on the basis of past work is expected to be robust against decoherence, would enable the encoding of very long sequences of entangled qubits.
We propose a method for producing entangled spin and orbital states in pairs of atoms resulting from the dissociation of diatomic molecules. The method employs the interference between a one-photon and a two-photon process to break the backward-forward symmetry of the dissociation processes. The spin entanglement of distant atom pairs makes use of excited spin-orbit-coupled (molecular) intermediate states. When the dissociating molecules are confined to a one-dimensional optical lattice, the method can be used to generate long sequences of (spin- and orbit-) entangled pairs of atoms.
Ultracold polar molecules possess a manifold of long-lived molecular rotational states, which can be coherently controlled using microwave fields and entangled by the long-range dipole-dipole interactions between molecules. The ability to control these features at the individual molecule level provides a rich toolbox with which to engineer quantum simulations of exotic materials or build a molecular quantum computer. Until recently, this level of single molecule control has eluded researchers due to the challenges inherent in taming the complex internal structure of molecules. In this thesis, we demonstrate full control over the internal quantum states and coherent interactions of individual NaCs molecules in optical tweezers. This platform is based on coherent assembly of ultracold Na and Cs atoms trapped and cooled in separate arrays, before being magnetoassociated at a Feshbach resonance to form weakly-bound molecules. Using high-resolution spectroscopy of electronically excited molecular states, we identify an efficient two-photon pathway to the rovibrational ground state of NaCs that we use to prepare an array of ground state molecules in tweezers. We demonstrate a "magic ellipticity'' technique to eliminate differential light shifts between two molecular rotational states and achieve coherence times of up to 250(40) ms for a superposition of those states. We then show that we can rearrange molecules in an array to eliminate defects and perform single-shot readout of multiple rotational states using controlled molecule dissociation and imaging of constituent atoms at high magnetic field. Finally, we coherently control the dipole-dipole interactions between two molecules, producing a Bell state with a fidelity of 94(3) % and demonstrating a universal entangling iSWAP gate for qubits encoded in molecular hyperfine states.
Generating entanglement between two Rydberg atoms is at the core of neutral-atom quantum computers. Current two-qubit gates operate in the Rydberg-blockade regime, in which the full strength of the van der Waals interaction between the two Rydberg atoms is not directly exploited, to avoid sensitivity to the position noise of the tweezer-trapped atoms, at the cost of a longer time spent in the Rydberg state. Here, we propose a set of techniques based on coherent control of the atomic motion obtained by combining optical tweezers and a two-dimensional optical lattice, and a sequence of multiple on/off pulses. The protocols keep the two-qubit gate error contribution from position noise below 10−410^{-4}10−4, heat the atom by less than~Δn=0.01Δn = 0.01Δn=0.01, while being robust to alignment errors of the potential up to 505050~nm and thermal excitation up to nˉ=3\bar{n} = 3nˉ=3. This toolbox opens the path for new two-qubit Rydberg gates directly, or partially, driven by the interaction, in which the atoms spend only ∼10\sim 10∼10~ns in the Rydberg state, minimizing the increasingly dominant error source originating from its finite lifetime.
The realization of rovibrationally stable dense samples of ultracold diatomic molecules remains one of the main stepping stones to achieve the next slate of major goals in the field of atomic and molecular physics. Though obtaining diatomic alkali molecules was seen as a logical next step following the optical cooling of atoms, many of the possible applications currently under investigation extend beyond atomic and molecular physics. For example, spectroscopy of ultracold molecules can help in testing extensions of the Standard Model via the search for a permanent electric dipole moment of the electron (1; 2), or the energy difference between enantiomers of chiral molecules (3). Various molecular transitions can be utilized to track the time dependence of fundamental constants, including the fine structure constant and the proton to electron mass ratio (4). They also open the way for cold and ultracold chemistry, where the interacting species and products are in a coherent quantum superposition state (5) and reactions can happen via quantum tunneling. Dipolar ultracold quantum gases promise to show a plethora of new phenomena due to anisotropic long-range dipole-dipole interactions (6). Dipolar molecules in optical lattices can be employed as a quantum simulator of condensed matter systems, and they are predicted to demonstrate new quantum phases such as a dipolar crystal, supersolid, checkerboard and collapse phases (7; 8). Ultracold polar molecules also represent an attractive platform for quantum computation (9). They offer a variety of long-lived states for qubit encoding, including rotational, spin and hyperfine (if electronic and nuclear spins are non-zero), Λ and Ω-doublet states (10) and scalability to a large number of qubits. Polar molecules can be easily controlled by DC electric and magnetic fields, as well as bymicrowave and optical fields, allowing the design of various traps (11; 12). The main appeal of polar molecules for quantum information processing, however, comes from their permanent electric dipole moment, permitting them to interact via a long-range dipole-dipole interaction. The dipole-dipole interaction offers a tool to construct two-qubit gates, required for universal quantum computation (9; 13). Ultracold molecules in their ground vibrational state v = 0 (and even in specific rotational, hyperfine or Zeeman states) are required formany of these applications since they have a large permanent electric dipole moment and are stable with respect to collisions and spontaneous emission. Currently translationally ultracold (100 nK 1 mK) molecules are produced by magneto(14) and photo-association (15) techniques. In a typical photoassociation scheme, 3
Recent theoretical and experimental advances have led to better understanding and control of simple molecules, bringing them to the forefront of quantum science. Diatomic polar molecules, with their vibrational and rotational degrees of freedom and electric dipole moment, are excellent candidates for a scalable qubit, probes of beyond-Standard Model physics, and quantum simulation of topological and chiral many-body systems. These applications call for high-phase space density (PSD) of molecules in a single quantum state. To date, the highest molecular PSD is achieved by coherently associating degenerate quantum gases of atoms into molecules. However, this requires fine-tuning of experimental parameters to maximize spatial overlap of the atomic density distributions while minimizing three-body recombination of the atoms.\nIn this thesis, we propose a bottom-up solution to gain single particle control of ultracold molecules for the first time. We use optical tweezers to deterministically assemble a single NaCs molecule in a single quantum state from a pair of Na and Cs atoms. Added benefits of using optical tweezers include: tight confinement of isolated atoms enabling cooling of Na and Cs to their quantum ground state of motion in less than 100~ms, and dynamic reconfigurability of optical tweezer arrays which will allow scaling up to defect-free arrays of single molecules. In the process, we realize a conceptually simple platform for studying atomic collisions and molecular spectra which derives its strength from the ability to gather "before" and "after" images of single atoms.