In the winter of 2017, the American Embassy in Havana was in a precarious state. The Embassy, a six-story tower that sits next to the seawall known as the Malecón, was built in 1953, and during the five decades in which diplomatic relations between Cuba and the United States were suspended it had suffered from neglect. Salt and humidity from the ocean ate away at the pins holding up the marble façade. Work crews erected a fence around the most vulnerable area, to insure that no one was impaled by shards of marble tumbling from the walls.

Audrey Lee, a career Foreign Service officer in her late forties, worked in a snug office on the ground floor. (The name is a pseudonym, which she requested in order to protect her privacy.) Her life in Havana was fascinating but orderly. She lived with her husband and their twelve-year-old twins in a quiet neighborhood full of diplomats, and drove an S.U.V. to work each morning, arriving habitually by seven-thirty. A veteran of several Foreign Service tours, she felt at ease in Cuba—except for one peculiar incident. Earlier that year, when the family returned to Havana from a vacation, they were struck by a foul stench in their kitchen. The freezer was unplugged. Lee and her husband cleaned out the rotten food, plugged the freezer in, and went back to their routine, thinking little about the fact that someone had been there while they were away.

On the evening of March 17th, Lee came home from the Embassy, made dinner, and ate with the twins in the kitchen nook. Her husband was away on business. Afterward, the kids went upstairs to play Minecraft. At around eight o’clock, Lee washed the dishes. The kitchen lights made it hard to see out the window, but she knew that there was a wooden booth outside where Cuban police kept watch. As Lee was cleaning, she felt a sudden burst of pressure in her head, then a stabbing pain worse than any she had ever experienced. Her breath quickened and she was overcome by panic. Lee had heard rumors around the Embassy of colleagues falling victim to mysterious “sonic attacks,” but no one knew what they were or what had caused them.

As the pain grew more intense, she remembered overhearing a security officer at the Embassy talking about how employees could protect themselves. “Get off the X,” he had said, which Lee took to mean move away from the site where she experienced the pain. She made her way to the family room and took a few minutes to steady herself. After checking on the twins, she went to her bedroom to lie down, but the pain kept her from sleeping.

The next morning, Lee’s head still hurt. At breakfast, her son asked her to read the ingredients on a box of cereal, and she struggled, moving the box back and forth as she tried to focus. In the coming weeks, she often felt dizzy and lost her balance, and sometimes walked into doors. She felt as if she were moving even when she was still, a sensation that she compared to walking after taking off roller skates. She was sleeping just an hour or two a night. Co-workers noticed that she was becoming forgetful. One afternoon, a colleague stopped by her office to discuss running an errand together. When the colleague returned five minutes later and said, “Are you ready?,” Lee looked up and said, “Ready for what?”

Wary of being seen as a burden, Lee didn’t mention her condition to her superiors, Jeffrey DeLaurentis, the Embassy’s chief of mission, and his deputy, Scott Hamilton, but they already knew that something strange was happening. Between December 30, 2016, and February 9, 2017, at least three C.I.A. officers working under diplomatic cover in Cuba had reported troubling sensations that seemed to leave serious injuries. When the agency sent reinforcements to Havana, at least two of them were afflicted as well.

All the victims described being bombarded by waves of pressure in their heads. Unlike Lee, though, the C.I.A. officers said that they heard loud sounds, similar to cicadas, which seemed to follow them from one room to another. But when they opened an outside door the sounds abruptly stopped. Some of the victims said that it felt as if they were standing in an invisible beam of energy.

The Americans suffered from headaches, dizziness, and a perplexing range of other symptoms. Later, specialists studied their brains and determined that the injuries resembled concussions, like those suffered by soldiers struck by roadside bombs in Iraq and Afghanistan. But there were no signs of impact. One of the specialists said it was as if the victims had a “concussion without concussion.” Douglas Smith, who oversaw a team that examined the victims at the University of Pennsylvania, said, “None of us have ever encountered anything like this before.” Experts at the C.I.A. were baffled by what they saw as an alarming new threat, one of the most confounding medical and espionage mysteries to involve American personnel overseas since the Cold War. The affliction didn’t have a name, so some of the victims started to refer to it simply as the Thing.

A year earlier, in March, 2016, Barack Obama had flown to Havana to celebrate the restoration of diplomatic relations between the United States and Cuba, after more than half a century of enmity. With Raúl Castro smiling in the audience at the venerable Gran Teatro, Obama gave a speech in which he announced that he had “come here to bury the last remnant of the Cold War in the Americas.”

The reconciliation had been at least four years in the making. In February, 2012, Senator Patrick Leahy, Democrat of Vermont, who had long favored restoring diplomatic relations with Cuba, had met with Raúl Castro in Havana. “Wouldn’t it be nice if our grandchildren could grow up in a world where our countries no longer treat each other as enemies, and our grandchildren could travel and study and learn to get along together?” Leahy said. A Cuban diplomat who attended the meeting recalled that Castro replied, “Tell Obama that we shouldn’t leave this situation to our children, that we have to solve this before I go.”

Not long after Obama was reëlected, in November, 2012, he asked Benjamin Rhodes, one of his closest national-security advisers, to lead secret negotiations with the Cubans. Rhodes knew little about Cuba and barely understood Spanish, so Ricardo Zúñiga, a National Security Council official who had previously served in Havana, was called in to work with him.

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Obama saw a diplomatic opening with the Cubans as something that would be “nice to have,” rather than something that “he had to have,” a former Administration official said. The stakes were significantly higher for Raúl Castro. In the past decade, Cuba’s economy had depended on subsidized oil, provided by President Hugo Chávez of Venezuela. But Chávez was dying of cancer, and the Cuban leadership was desperate for new sources of revenue. When Raúl Castro chose his son, Alejandro, to serve as his intermediary with the Obama Administration envoys, Zúñiga felt assured that the Cubans were serious about negotiating an agreement.