Quantum Control of a Single H2+ Molecular Ion

Science is founded on the benchmarking of theoretical models against experimental measurements, with the challenge that, for all but the simplest systems, the calculations required for high precision become extremely challenging. <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msubsup><a:mi mathvariant="normal">H</a:mi><a:mn>2</a:mn><a:mo>+</a:mo></a:msubsup></a:math> is the simplest stable molecule, and its structure is calculable to high precision. However, studying <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:msubsup><d:mi mathvariant="normal">H</d:mi><d:mn>2</d:mn><d:mo>+</d:mo></d:msubsup></d:math> experimentally presents significant challenges: Standard control methods such as laser cooling are not applicable due to the long lifetimes of its rotational and vibrational states. Here, we solve this issue by combining buffer gas cooling to quench the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msubsup><g:mi mathvariant="normal">H</g:mi><g:mn>2</g:mn><g:mo>+</g:mo></g:msubsup></g:math> rovibrational excitation with quantum logic operations between <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"><j:msubsup><j:mi mathvariant="normal">H</j:mi><j:mn>2</j:mn><j:mo>+</j:mo></j:msubsup></j:math> and a cotrapped “helper” ion to control the molecule’s hyperfine structure. This enables us to perform pure quantum state preparation, coherent control, and nondestructive readout, which we use to demonstrate high-resolution microwave spectroscopy in the hyperfine structure of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msubsup><m:mi mathvariant="normal">H</m:mi><m:mn>2</m:mn><m:mo>+</m:mo></m:msubsup></m:math> with a precision of 2 Hz. Our results pave the way for high-precision spectroscopy of <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"><p:msubsup><p:mi mathvariant="normal">H</p:mi><p:mn>2</p:mn><p:mo>+</p:mo></p:msubsup></p:math> in both the microwave and optical domains. Because of the wide applicability of buffer gas cooling, our method provides a general tool for molecular ion species that are hard to control with quantum logic tools alone.