Jonathan Toebbe and his wife Diana were arrested in West Virginia on Saturday, the Justice Department announced.
They allegedly tried to sell nuclear submarine design data, hidden in a peanut butter sandwich, to someone they thought represented another country.
In fact, it was an undercover FBI agent.
According to the statement, Mr Toebbe and his partner – 42 and 45 respectively – have now been charged under the Atomic Energy Act.
Mr Toebbe worked in the US Navy’s nuclear propulsion programme and had national security clearance. His wife is a high school teacher.
The Justice Department said that in April 2020 he sent a package to an unnamed foreign government containing restricted data and a message suggesting a covert relationship, so that they could buy more data from him.
He then allegedly began writing to an individual by encrypted email. While he thought this person represented the foreign government, they were actually an FBI agent, the affidavit said.
After several months, the accused couple allegedly made a deal to share secret information in exchange for around $100,000 (£73,000) in cryptocurrency.
In June this year, Jonathan and Diana Toebbe travelled to West Virginia to drop off the data.
With Diana acting as a lookout, Jonathan “placed an SD card concealed within half a peanut butter sandwich” at a determined location, the affidavit said.
After the agent collected the card, they sent payment and received a decryption key to access the SD card. On it was restricted data “related to submarine nuclear reactors”.
Mr Toebbe then performed a second so-called dead drop – this time hidden inside a chewing gum packet – in August, with yet more secret data on it.
FBI agents then arrested the couple on Saturday, during a third dead drop.
The couple are set to appear in federal court on 12 October.