Quantum Sculpting

Halina H. Rubinsztein-Dunlop

Sculpted light refers to the generation of custom designed light fields. These light fileds can be applied in many diverse fields ranging from interrogating single atoms or atom assembly to using these fields for optical micromanipulation and optical tweezers as well as creating new quantum devices and sensors. We consider here the study and application of light with structured intensity, polarization and phase. We can create custom fields in multiple planes using dynamic and geometric phase control. As an example, the use of sculpted light in imaging has led to superresolution microscopy developed by Betzig, Hell and Moerner (2014 Nobel prize in Chemistry). Sculpted light can be generated using several technologies. These are spatial light modulators (SLM) and Digital Micromirror Devices (DMD) that enable the production of configurable and flexible confining potentials at the nano and micron-scale. Sculpted light can also be produced using time averaged methods such as Acousto-Optics Modulators (AOM), enabling production of highly configurable time-averaged traps. All these methods achieve dynamical and flexible sculpted light fields and enable imaging of the amplitude patterns, phase and polarization. Using these sculpted light we can produce novel optical potentials which can be used for intricate studies of light -matter interactions in a variety of environments. We will describe their use ranging from studies such as quantum thermodynamics using ultra cold atoms to trapping and manipulating nano and micron-size objects or even making measurements in-vivo inside biological cells.

Amber Scoon

Patrick McQuillen

The sculpting of ultracold neutral plasmas represents a frontier in the experimental study of collective modes in strongly coupled plasmas. By extending the range of accessible length scales to less than tens of microns we gain access to a regime where The sculpting of ultracold neutral plasmas represents a frontier in the experimental study of collective modes in strongly coupled plasmas. By extending the range of accessible length scales to less than tens of microns we gain access to a regime where strong coupling's effects are predicted yet largely untested. To this effort, high resolution optical systems were designed, bench tested and implemented for sculpting and imaging ultracold neutral plasmas. Many complications and unexpected effects were documented to assist future experimental design considerations, including, those due to saturation and optical thickness, both of which limit the utility of 461 nm push beam modulations. It was concluded that sculpting should be performed on the 412 nm ionizing beam and real-time density space analysis is reliable for spatial frequencies up to 5 cyc/mm by using 4X magnified imaging. Higher spatial frequencies benefit from velocity space analysis due to extremely fast dynamics and low intensity levels.

A. Goswami

Scott Aaronson, Shalev Ben-David

Given a problem which is intractable for both quantum and classical algorithms, can we find a sub-problem for which quantum algorithms provide an exponential advantage? We refer to this problem as the "sculpting problem." In this work, we give a full characterization of sculptable functions in the query complexity setting. We show that a total function f can be restricted to a promise P such that Q(f|_P)=O(polylog(N)) and R(f|_P)=N^{Omega(1)}, if and only if f has a large number of inputs with large certificate complexity. The proof uses some interesting techniques: for one direction, we introduce new relationships between randomized and quantum query complexity in various settings, and for the other direction, we use a recent result from communication complexity due to Klartag and Regev. We also characterize sculpting for other query complexity measures, such as R(f) vs. R_0(f) and R_0(f) vs. D(f). Along the way, we prove some new relationships for quantum query complexity: for example, a nearly quadratic relationship between Q(f) and D(f) whenever the promise of f is small. This contrasts with the recent super-quadratic query complexity separations, showing that the maximum gap between classical and quantum query complexities is indeed quadratic in various settings - just not for total functions! Lastly, we investigate sculpting in the Turing machine model. We show that if there is any BPP-bi-immune language in BQP, then every language outside BPP can be restricted to a promise which places it in PromiseBQP but not in PromiseBPP. Under a weaker assumption, that some problem in BQP is hard on average for P/poly, we show that every paddable language outside BPP is sculptable in this way.