President Trump and North Korean leader Kim Jong Un stand together on North Korean soil on Sunday. (Brendan Smialowski/AFP/Getty Images)

As the TV spectacle of President Trump’s first visit to North Korea fades, his top diplomats are left with the same daunting challenge that bedeviled them before: a hostile dictatorship that views its expanding nuclear arsenal as critical to its survival.

Secretary of State Mike Pompeo and his special envoy, Steve Biegun, have been given two to three weeks to start new talks with their North Korean counterparts aimed at making a breakthrough in stalled denuclearization negotiations.

While the disputes remain the same, the administration hopes that the chemistry on display between Trump and North Korean leader Kim Jong Un on Sunday will unlock a spirit of cooperation that has been absent from engagements between North Korean negotiators and U.S. officials below the rank of president.

“The president, by getting together with Chairman Kim today, broke through and was able to get us the opportunity to get back to the negotiating table, which I’m excited about,” Pompeo told reporters before flying back to Washington.

But absent a change in the U.S. negotiating position, it is unclear if the connection Trump made with Kim during a brief walk on North Korean soil and a 50-minute meeting Sunday will bridge the wide chasm between Washington and Pyongyang.

Pompeo told reporters Sunday that economic sanctions will stay in place, setting aside a key demand by North Korean officials that the United States provide at least partial relief in parallel with their steps to denuclearize.

Biegun also pushed back against the idea that the United States has altered its previous demands, saying in a statement, “We are not preparing any new proposals currently.”

Experts say U.S. officials should focus on reaching a shared understanding with North Korea of what denuclearization would look like and getting a better assessment of Pyongyang’s nuclear weapons inventory.

“This starts to look real when they get a veritable declaration of all weapons and facilities from the North. That declaration could come in pieces, but it has to happen,” said Victor Cha, a North Korea expert at the Center for Strategic and International Studies.

Critics of the Trump administration’s negotiations say the president is misreading Kim, who has shown no desire to abandon his nuclear and missile arsenal.

“Despite two U.S.-North Korean summits and repeated efforts at engagement, there is still not even an agreed-upon definition of ‘denuclearization,’ ” said Bruce Klingner, a North Korea expert at the conservative Heritage Foundation.

But others offered cautious praise for Trump’s approach.

“I’m not opposed to this,” Mintaro Oba, a former State Department official, said in a statement. “Offering a purely optical meeting to Kim Jong Un, without raising expectations for specific deliverables, helps reinforce a narrative of the United States acting in good faith to advance diplomacy. And it may expand Kim’s domestic space to engage.”

One variable that is expected to change in the Trump administration’s favor is the leader of North Korea’s negotiating team. Pompeo said Sunday that the North Korean Foreign Ministry would be leading the talks for the country. “I don’t know exactly who from the Foreign Ministry, but it’s likely to be one of a couple people,” he said.

One potential counterpart for Biegun is North Korean Vice Foreign Minister Choe Son Hui, a seasoned diplomat with years of experience working with American officials on denuclearization issues. Previously, when the Foreign Ministry was sidelined from the talks, Kim entrusted the negotiations to his former spy chief, Kim Yong Chol, a longtime hawk who came off as inscrutable and arrogant during meetings with Pompeo and his aides, U.S. officials said.

While fresh blood could help the negotiations, the United States and North Korea have thus far proved unable to advance the talks outside of meetings between Trump and Kim.

“This is the first time there have been real working-level negotiations that weren’t part of a summit,” said Joel Wit, a nonproliferation expert at the Stimson Center.

The Trump administration has adamantly denied that it is loosening its demands on North Korea, in particular its stance that economic sanctions will stay in place until the country fully denuclearizes, raising questions about how it will move discussions forward.

On Monday, Trump’s national security adviser, John Bolton, decried a report in the New York Times suggesting that the administration is pursuing an interim deal that would accept the North as a nuclear power and exchange a freeze on nuclear development for partial sanctions relief.

“Neither the [National Security Council] staff nor I have discussed or heard of any desire to ‘settle for a nuclear freeze by NK,’ ” he tweeted. “This was a reprehensible attempt by someone to box in the President. There should be consequences.”

Bolton was noticeably absent from the historic meeting between Trump and Kim on Sunday as he flew that day to Mongolia. During the Hanoi summit in February, Trump prevented Bolton from attending a high-level dinner over concerns he could hurt the mood of the talks. Bolton has tangled with Biegun in the past over negotiating strategy.

Biegun has appeared to be more amenable to providing concessions to North Korea in exchange for significant steps toward denuclearization, an approach some have called “action for action.”

On Friday, Biegun told his South Korean counterpart, Lee Do-hoon, that the Trump administration was seeking “simultaneous, parallel” progress with North Korea in implementing an agreement that Trump and Kim reached in their summit last year in Singapore. In contrast, Bolton has pushed Trump to pursue an all-or-nothing approach that would require North Korea to give up its entire arsenal in one agreement in exchange for full sanctions relief, a proposal Pyongyang has long rejected.

In the absence of a new negotiating strategy, it’s unclear if even a modest breakthrough will occur. But with the next talks set to take place before August, the two sides will be put to the test soon.

“The only thing new on this iteration of diplomacy is the bromance,” Cha said. “We have lifted sanctions before to no effect. But Trump is trying to gain Kim’s trust.”