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# Welcome to the Ion Trap Group at UC Berkeley
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#### Department of Physics, University of California, Berkeley <br/> Berkeley Nanosciences and Nanoengineering Institute
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<divid="affiliations">
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Department of Physics, University of California, Berkeley <br/>
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Berkeley Nanosciences and Nanoengineering Institute
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</div>
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We trap ions to investigate various aspects of quantum physics and quantum information. The motion of trapped ions can be accurately controlled in the quantum regime. Together with the ions' excellent quantum memory capabilities, trapped ions are thus an excellent system to investigate experimental quantum information processing. Furthermore, we couple the motion of trapped ions to bulk materials to learn more about the quantum properties of mesoscopic systems. See our
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research tab for more information about specific projects.
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We have a limited number of undergraduate research positions available! If you are interested, please send your CV and transcript to Hartmut Haeffner ([email protected]).
<b>Illustration of verification protocols for analog
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quantum simulators.</b> Various protocols yield information
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about the accuracy of a quantum simulator by propagating
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a state along a closed loop and verifying to what degree the
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system returns to its original state, labeled here as |0⟩.
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The state |ψ⟩ denotes the state of the system after applying the dynamics of Hamiltonian <i>H</i>
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for a time τ, whereas the state |ɸ⟩ denotes an arbitrary state.
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<br/>(a) <i>Time-reversal analog verification:</i> Running an analog simulation forward in time, followed by the same analog simulation backward in time.
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<br/>(b) <i>Multi-basis analog verification:</i> Running an analog simulation forward in time, rotating the state, performing the
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backward simulation by an analog version in the rotated basis, and finally rotating the state back.
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<br/>(c) <i>Randomized analog verification:</i> Running a random sequence of subsets of the Hamiltonian terms
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(denoted as <i>H</i><sub>rand</sub>), followed by an inversion sequence of subsets of the Hamiltonian terms which has been
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calculated to return the system approximately to a basis state.
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</caption>
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<TR><TD><imgsrc="/research/quantum-emulation/verification-protocols.png"alt="Illustration of verification protocols for analog quantum simulators"width="500"></TD></TR>
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</table>
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<figure>
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<img src="/research/quantum-emulation/verification-protocols.png" alt="Diagrams of verification protocols for analog quantum simulators" width="500" />
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<figcaption>
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<b>Illustration of verification protocols for analog
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quantum simulators.</b> Various protocols yield information
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about the accuracy of a quantum simulator by propagating
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a state along a closed loop and verifying to what degree the
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system returns to its original state, labeled here as |0⟩.
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The state |ψ⟩ denotes the state of the system after applying the dynamics of Hamiltonian <i>H</i>
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for a time τ, whereas the state |ɸ⟩ denotes an arbitrary state.
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<br/>(a) <i>Time-reversal analog verification:</i> Running an analog simulation forward in time, followed by the same analog simulation backward in time.
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<br/>(b) <i>Multi-basis analog verification:</i> Running an analog simulation forward in time, rotating the state, performing the
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backward simulation by an analog version in the rotated basis, and finally rotating the state back.
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<br/>(c) <i>Randomized analog verification:</i> Running a random sequence of subsets of the Hamiltonian terms
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(denoted as <i>H</i><sub>rand</sub>), followed by an inversion sequence of subsets of the Hamiltonian terms which has been
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calculated to return the system approximately to a basis state.
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</figcaption>
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</figure>
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## Precision measurements using trapped ions
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local Lorentz invariance of the electron using calcium ions by factor of two to about 5e-19.
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