{"id":28,"date":"2017-12-13T15:54:33","date_gmt":"2017-12-13T20:54:33","guid":{"rendered":"http:\/\/sites.williams.edu\/ion\/?page_id=28"},"modified":"2025-05-28T15:16:41","modified_gmt":"2025-05-28T19:16:41","slug":"research","status":"publish","type":"page","link":"https:\/\/sites.williams.edu\/ion\/research\/","title":{"rendered":"Research"},"content":{"rendered":"

Quantum mechanical phenomena are in general impossibly difficult to simulate on an ordinary computer.\u00a0 To see why, consider the simplest quantum system imaginable: a single particle with two states which we might label |0> and |1>.\u00a0 For an arbitrary state
\n|\u03a8> of this system we might write<\/p>\n

|\u03c8> =\u00a0\u03b1|0> +\u00a0\u03b2|1>,<\/p>\n

i.e. there are two `weights’\u00a0\u03b1 and\u00a0\u03b2 which describe the probability that we might ultimately find our particle in |0> or |1>, respectively, if we were to measure it.\u00a0 So, we need two weights to write down our general state |\u03c8>.\u00a0 Simple enough, but it turns out that things get more complicated if we add particles to our system.\u00a0 If we had three of these particles and measured their state, we might find all three to be in the state |0>, which we might write as |000>.\u00a0 But, we might also measure |001>, or |010>, or any of the other possible combinations – there are eight possibilities in total.\u00a0 So, to write down the general state of the system we would now have to write<\/p>\n

|\u03c8> =\u00a0\u03b1|000> +\u00a0\u03b2|001> + \u03b3|010> + . . . + \u03b8|111>;<\/p>\n

|\u03c8> now spans a space with eight `basis states,’ and eight weights are needed to write it down.\u00a0 More generally, for N particles there are 2N<\/sup> weights.\u00a0 As a result, calculations involving quantum systems slow down exponentially with system size.<\/p>\n

Fortunately, quantum mechanics offers some alternative ways to circumvent the problem.\u00a0 In the Doret lab we are interested in\u00a0analog quantum simulation<\/em>, wherein one quantum system is used to emulate the interactions and behavior of a second system which is challenging or impractical to study in its native form.<\/p>\n

Trapped Ion Quantum Simulation<\/strong><\/h3>\n

Atomic ions are a good choice to use as the `engine’ for such a quantum simulator.\u00a0 The ions’ charge gives us a handle with which to hang on to them in electromagnetic traps, and laser or microwave fields can be used to manipulate and control the ions’ states.\u00a0 Our goal is to perform simulations based around the vibrational degrees of freedom of the transverse motion of a chain of trapped ions.<\/p>\n

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Ion configuration for studying heat flow.<\/p><\/div>\n

As one example, we are working towards an investigation of thermal conductivity at mesoscopic scales such as those found in modern digital electronics.\u00a0 By using laser-cooled ions to implement thermal reservoirs at each end of a chain of ions we plan to measure the flow of energy along the chain.\u00a0 We ultimately plan to tailor the interaction between these ions’ vibrations and their internal states to simulate disordered materials and study the onset of Fourier’s Law thermal gradients at the nanoscale.\u00a0 Along the way we plan to study methods for improving the cooling rates of slowly cooled modes in sympathetically cooled ion chains, a problem likely to be critical developing large-scale trapped ion quantum information processors in the years to come.<\/p>\n

Precision Measurement<\/strong><\/h3>\n

Trapped ions are also a wonderful system for pursuing precision measurements; few systems do a better job of approximating the ideal of a single, isolated atoms free of external perturbations.\u00a0 Measurements in systems of trapped ions are thus central to improvements in precise metrology, searches for New Physics, and probing atomic and nuclear structure.<\/p>\n

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2D King Plot of the Ca+ 866 nm transition isotope shifts (from PRL 115, 053003 (2015)) against our recent 729 nm E2 transition isotope shift measurement<\/p><\/div>\n

Motivated in part by our plans to use electric quadrupole transitions for `thermometry’ in our planned study of the onset of Fourier’s Law, our lab has been pursuing precise measurements of isotope shifts in forbidden transitions in Ca+<\/sup>.\u00a0 These shifts are central to determinations of nuclear charge radii.\u00a0 Additionally, isotope shifts for different transitions in the same set of nuclei are linearly related to first-order.\u00a0 Searches for non-linearities in this relationship are sensitive to both to Standard Model physics such as nuclear polarizabilities and possible new, Beyond Standard Model interactions.<\/p>\n

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Laboratory Setup<\/strong><\/p>\n

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`Gen V’ ion trap from GTRI<\/p><\/div>\n

Most of our experiments have taken place within a surface electrode ion trap designed and fabricated by the Georgia Tech Research Institute.\u00a0 Surface electrode traps typically feature many control electrodes located close to the trapped ions, enabling precise tailoring of confining potentials and trapping of ions in multiple zones of the trap.\u00a0 Our trap has approximately ninety electrodes, each individually controlled.<\/p>\n

To load and trap ions we resistively heat an oven loaded behind the traps `loading slot’ to produce a beam of neutral calcium ions.\u00a0 These ions stream through the slot\u00a0and\u00a0can then be photoionized and trapped by a combination of static and oscillating electric fields.\u00a0\u00a0The trap is maintained under ultra-high vacuum in a stainless steel chamber with viewports that permit laser access over the trap surface.\u00a0\u00a0A large, home-built lens collects approximately 5% of the light emitted by the ions and images it onto a CCD camera and a PMT.<\/p>\n

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Schematic view and photograph of our trap setup.<\/p><\/div>\n

Trapping calcium ions requires a number of lasers for photoionization, Doppler cooling, state preparation, and coherent manipulation.\u00a0 One of the nice features of calcium is that all essential transitions are at wavelengths for which optical fibers and laser diodes are readily available.\u00a0 We thus use home-built lasers and control electronics throughout the lab, including a simple, very low noise piezo driver of our own design.\u00a0 To ensure our lasers remain locked to the correct wavelengths we use a scanning Fabry-Perot cavity to transfer the stability of a commercial stabilized HeNe onto our diode lasers.\u00a0 Acousto-optic modulators can then be used to control the frequency, intensity, and duration of laser pulses used to cool, manipulate, and interrogate the trapped ions.<\/p>\n

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Bless loads Sr into the blade trap vacuum chamber during summer 2023.<\/p><\/div>\n

In newer work, we have been bringing online a suite of lasers to add strontium ions to the mix as we look to demonstrate rectification of thermal energy flow in ion chains.\u00a0 Our plan is to co-trap Sr and Ca ions in a macroscopic blade trap, designed by Matthew Roychowdhury ’21 and placed under vacuum by Bless Bah Awazi ’24 and Sam Bishop ’25.<\/p>\n

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Student Research Participation<\/strong><\/h3>\n
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Cole Meisenhelder ’15 in the shop<\/p><\/div>\n

At Williams undergraduate researchers play a central role in moving research projects forward.\u00a0 This is especially so in the Doret lab; with so much of our equipment has been home-built, students are involved with every aspect of the work ranging from designing and assembling the tools we use to taking data in the laboratory and then analyzing it and preparing it for publication.\u00a0 To offer a few examples from recent thesis projects:<\/p>\n

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