Jay Taylor, a veteran American diplomat, and several family members who were visiting him gathered in the wood-panelled library of his sprawling, two-story residence in a corner of Havana once known as Country Club Park. The room had dark mahogany walls, one of which was decorated with a folding Chinese painting of a forest landscape. Taylor’s guests, dressed for dinner, sat on white sofas and matching chairs, chatting about their trip, which included a tour of Old Havana and a day on the white-sand beaches in Varadero.

It was the cocktail hour. As the sun set outside, a Cuban butler entered the room carrying a tray of freshly made mojitos. Taylor and his brother-in-law, David Rose, each took a glass and raised them for a toast. “Salud,” they recalled saying. As Rose brought his glass up for a sip, it shattered into pieces, spilling rum, lime, and mint on the marble floor. “Oh, my God, what’s happened here?” Taylor remembered asking Rose, who was alarmed but unharmed. Taylor made a joke about “bad Marxist-made glass.” Everyone laughed.

It was Christmas week, 1987, thirty years before American spies and diplomats reported coming under “attack” in Havana last year from what some investigators and doctors believed was a type of directed-energy device that caused injuries similar to concussions.

The incident with the mojito glass occurred just months after Taylor arrived in Havana as America’s top diplomat, inheriting the Ambassador’s residence, which was, according to lore, built as the “winter White House” of President Franklin Roosevelt. The coral limestone structure had a tennis court and a swimming pool. Relations between the United States and Cuba were, as always, fraught. Taylor favored deepening engagement with the Cuban regime, a position which put him at odds with Reagan Administration hawks in Washington, who took a dimmer view of Havana’s intentions—much like Jeffrey DeLaurentis, who, as Donald Trump took office, served as the chief of the U.S. diplomatic mission in Havana, when the current wave of mysterious incidents started.

Taylor wasn’t naïve, of course, to the Cuban espionage threat. Before the Marine Corps veteran took the assignment in Havana, he served on the White House National Security Council and as the Deputy Assistant Secretary of State for the State Department’s Bureau of Intelligence and Research, under Ronald Reagan. Though he didn’t say anything to his family at the time, Taylor knew they were being monitored, and that the residence was wired with listening devices and tiny cameras, which allowed Cuban intelligence officers to spy, in real time, on everything going on inside. “They knew us intimately,” Taylor assumed.

Initially, the shattered mojito glass seemed to be nothing more than some kind of “freakish event,” Taylor told me. Then, a couple of days later, his wife, Betsy, was in one of the upstairs bedrooms, talking with her mother, Sally Turner, when they heard a sharp cracking sound. An ornamental vase, which had been sitting on the dresser drawer, was cracked open. After the vase incident, Taylor suspected foul play by Cuban intelligence officers, who had a compound across the street from the Ambassador’s residence. The Cubans were so close that Taylor’s daughter, Laurie Peck, said when the mansion’s upstairs windows were open she could hear them chatting.

Taylor knew that the Cuban secret police routinely harassed U.S. diplomats and spies on the island. During his tenure, a Cuban surveillance team threw oranges and rocks at William Brencick, a State Department human-rights officer, while he was riding his white Puch racing bike. Brencick, who jumped off and fled into a cane field with his bike in hand, suspected that the Cubans had grown impatient tailing him at slow speeds, through the streets of Havana and its environs, and decided to remind him “who’s boss.” Jason Matthews, who served under Taylor as the C.I.A.’s Havana station chief, recalled how he would walk from his bedroom into the living room some mornings and find cigarette butts in the ashtray on his coffee table, a sign that a Cuban “entry team” had visited, uninvited, overnight and wanted him to know that they had been there.

Just as DeLaurentis did after at least three C.I.A. officers reported experiencing strange sensations of sound and pressure that left them injured, Taylor lodged a formal complaint with the director general of the U.S. division of the Cuban Foreign Ministry. Taylor couldn’t understand why his residence would be targeted with a new form of harassment. The Cuban leadership supported his efforts to expand engagement. Moreover, any attacks on American diplomats in Cuba would provide ammunition to hard-liners in the United States who favored increasing the Castro regime’s isolation. After his visit to the Foreign Ministry, Taylor assumed that the strange incidents would stop.

At the end of Christmas week, on the family’s last night in the Ambassador’s residence, Peck dressed her three-and-a-half-year-old son, Myles, for bed, in red pajama bottoms and a white knit top. She took him to one of the bathrooms to brush his teeth. After the boy finished, she handed him a glass of water so that he could rinse his mouth. The glass shattered in Myles’s hands, slicing his lips.

Taylor assumed the Cubans had been watching Myles through a tiny camera hidden in the bathroom, and, using a device of some kind, targeted the glass. Taylor stormed over to the Foreign Ministry and told his Cuban counterpart that it “looked like these incidents were aimed” at his family. The ministry official told Taylor that he was very sorry to hear about what had happened to his grandson. He insisted that the Cuban government wasn’t involved in any way.

The State Department dispatched a “sweep team,” made up of counterintelligence experts, to search the residence for eavesdropping devices and other clues. At the time, Matthews, the C.I.A.’s Havana station chief, who later authored the “Red Sparrow” spy-novel trilogy, surmised that the Cubans had used some sort of sonic or directed-energy device to shatter the glass and ceramic items. In addition to the three incidents at the Ambassador’s residence, Matthews came home one day to discover that the glass-topped table at his home had been shattered. One theory, which Taylor and Matthews seized upon, was that the Cubans had used Russian technology to break the items. (The Russians invested heavily in such devices during the Cold War, and, in the nineteen-seventies, bombarded the U.S. Embassy in Moscow with microwaves. Years later, the National Security Agency picked up intelligence about a “hostile” country, which it declined to identify by name, developing “a high-powered microwave system that may have the ability to weaken, intimidate, or kill an enemy over time and without leaving evidence.” The N.S.A. said it never confirmed if the weapon, in fact, existed, according to a 2014 statement to the Washington lawyer Mark Zaid, who now represents several of the government employees who were mysteriously sickened in Cuba and China.)

To try to catch the Cubans, members of the American security team placed sensors in and around Taylor’s residence. Taylor and Matthews doubted anything would be found, because they knew that Cuban intelligence officers could simply turn off any electronic devices to prevent them from being detected, or else remove them when the house was vacant. As expected, the sensors detected nothing out of the ordinary. No additional glasses or vases shattered. If the Cubans had a high-energy weapon, the Americans never found it. Some officials later questioned whether the incidents were caused by the Cubans or by other factors, such as poorly made glassware or weather anomalies.