Havana, Cuba (CNN) -- When Jimmy Carter arrived on his last visit to Cuba in 2002, Fidel Castro himself was on the tarmac to greet the former U.S. president.
He became the only American leader -- in or out of office -- to visit this island since Castro's 1959 revolution.
On Monday, Carter will be back on a private mission at the invitation of the Cuban government. He will meet with the new president, Raul Castro, and other officials to talk about bilateral ties.
The trip has sparked speculation that Carter could try to secure the early release of American contractor Alan Gross, who was recently sentenced to 15 years in a Cuban prison for "subversive" work providing illegal internet access to Cuban groups.
Carter's three-day trip is "to learn about new economic policies and the upcoming Party Congress, and to discuss ways to improve U.S.-Cuba relations," according to a press release from the Carter Center.
In some ways, the time is ripe.
Raul Castro has introduced sweeping changes to the Soviet-style economy, laying off state workers and expanding the private sector.
And just this week, Cuba freed the last of 75 dissidents jailed in a 2003 crackdown on the opposition that prompted worldwide condemnation.
Oscar Elias Biscet was one of those recently freed. He was originally sentenced to 25 years in prison for counter-revolutionary activities.
"I want to continue my work in the defense of human rights," he told CNN. "We want a democratic and free society."
Raul Castro agreed to release the prisoners last year as part of a deal brokered by the Catholic Church and Spain. Initially, only those who agreed to go into exile in Spain were freed.
But over the last couple of months, dissidents who demanded to stay in Cuba were also let go, removing one of the major obstacles to improved relations with the United States.
But Washington's response has been muted.
"The release of political prisoners is a step in the right direction," said U.S. State Department Deputy spokesman Mark Toner. "However, human rights conditions in Cuba remain poor. The Cuban government continues to limit fundamental freedoms, including freedom of speech, the press and peaceful assembly."
U.S. President Barack Obama singled out Cuba for criticism during a speech on regional policy in Chile earlier this week. He said it was time for Cuba to reciprocate on positive steps he had taken.
"Cuban authorities must take meaningful actions to respect the basic rights of the Cuban people -- not because the United States insists on it, but because the people of Cuba deserve it," he said.
Part of the reason for the impasse between the nations is Gross. The USAID contractor was arrested in Havana in 2009.
The United States said he was helping the Jewish community connect to the internet, but Cuba says he was part of a broad plot to use illegal internet connections to destabilize the government.
Despite the hefty 15-year-sentence, foreign diplomats in Havana have speculated that Gross could be released early as a humanitarian gesture, given that his mother and daughter are battling cancer.