After the rebels are captured in Cloud City, there is a scene where it is clear the Darth Vader tortures Han Solo. Later after the fact, Han makes it clear that it wasn't an interrogation because he tells Chewbacca that they didn't ask him any questions.
Darth Vader is not a good person but he doesn't seem to be a sadist (like Jabba for example), so what was purpose of torturing Han?
Han and Leia were tortured so that Luke would sense their suffering through the Force and come to rescue them. It was purely a move to trap Luke. When Luke was preparing to leave Dagobah and arguing with Yoda and ghost Obi-Wan about it, Obi-Wan pointed this out.
OBI-WAN: It is you and your abilities that the Emperor wants. That is why your friends are made to suffer.
The Official StarWars.com biography for Han Solo offers a stark explanation of the reason why Han was tortured;
"Han was tortured by Darth Vader, who used the pilot’s pain to lure Luke into a trap, and was later frozen in carbonite."
This is backed up by the Darth Vader biography which states;
"Vader tortured Han in an effort to lure Luke to Bespin, and later had Solo frozen in carbonite."
This is confirmed in the film itself when Obi-Wan tells Luke that he's walking into a trap:
OBI-WAN: It is you and your abilities that the Emperor wants. That is why your friends are made to suffer.
and in the film's novelisation
‘He doesn’t want you at all,’ Lando said. ‘He’s after someone called Sky walker.’
The two prisoners caught their breath at the casual mention of that name.
Han seemed puzzled. ‘Luke? I don’t get it.’
The princess’s mind was racing. All the facts were beginning to fit together into a terrible mosaic. In the past, Vader had wanted Leia because of her political importance in the war between Empire and Rebel Alliance. Now she was almost beneath his notice, useful only for one possible function.
‘Lord Vader has set a trap for him,’ Lando added, ‘and-‘ Leia finished his statement. ‘We’re the bait.’
The 'Star Wars: Empire Strikes Back Radio Dramatization' also offers a different and additional reason that Han was singled out for extra torture, as punishment for his insolence toward Vader.
Han [to Lando]: I'm sorry too
Vader: Not as sorry as you're going to be, Captain Solo. For every insult, you will scream a dozen times!
[Cut to]
Han: [IN THE NEXT ROOM. SCREAMS INTERMITTENTLY AS HE'S TORTURED]
Lando: What're they doing in there? Where's Han, Fett?
Fett: Lord Vader is . . . chastising him, Calrissian.
To reiterate and expound on what has been said: The point was to get Luke to come to Cloud City and walk into a trap. If Luke's vision was of Han and Leia having a nice time with Han's old friend, why would Luke feel compelled to save them? So when Han says
They never even asked me any questions
and Leia says
Why are they doing this to us?
it is because Vader knows Luke won't show up unless he senses that his friends will be in pain. Lucas actually explains this in the documentary Empire of Dreams.
Wookieepedia Legends page:
Three years after the Battle of Yavin, Darth Vader again tortured Leia Organa, as well as Han Solo and Chewbacca, on Cloud City. While the torture was not augmented by the Force, Vader knew that their anguish would reach Luke Skywalker through the Force and draw him to Bespin where he could be captured and delivered to Emperor Palpatine. Han was subjected to the scan grid, Chewie to sonic torture and searing lights. Leia, like Han, went through an ordeal with a torture machine, though the specific details are unknown.
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Wookieepedia Canon page:
Darth Vader was adept at it: even as a Jedi, he Force choked Poggle the Lesser to gain information on killing the brain worms. He once tortured Han Solo so his pain would reverberate through the Force and draw out Luke Skywalker.
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Oddly enough, in the original draft of the script by Leigh Brackett, Vader doesn't torture anyone. In fact, Leia, Han, Chewie, and Lando sit down at the table and have a meal with Vader. Leia asks why he is being so nice to her compared to the treatment she got on the Death Star, and Vader says:
You’re forgetting something, Princess. When we entertained you aboard the Death Star, you had information that we needed. Now you have nothing.
Leia says she doesn't understand why he is there if he doesn't want anything from them. Vader mentions Luke. Then this exchange happens:
LEIA
But I don’t know where he is... or even if he’s still alive.DARTH VADER
He’s alive. And he’ll find you, because he loves you.HAN
That’s ridiculous. He could search for...DARTH VADER
He’ll find her. And until then, we wait. I would advise you against any rash moves. I’ve set a guard on the Falcon so there’s no escape that way. I shan’t lock your doors unless you make it necessary.LEIA
Luke hasn’t the faintest idea where we are. You must be out of your mind.DARTH VADER
Then there’s no need to worry, is there?
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Darth Vader tortured him so Luke would sense it through The Force. It was just to lure Luke there so that Darth Vader could try to bring him to the Dark Side.
Probably trying to get to Luke. He was also testing if the 'carbon-freezing' would work.He did carbon-freeze him at the end and gave his body away as a reward.
The official answer is, as stated above, that Vader made them suffer so that Luke would fee it through the force and come to rescue them. they were bait.
However, consider this: If a Jedi/Sith as powerful as Vader was wanted answers, he could mind probe someone. Obi wan made it clear in the first movie that such mind-tricks were more effective on the weak minded. But IMHO I bet that under duress such as torture, a stronger mind would be just as vulnerable. Maybe Vader DID "ask" the questions, just not verbally, if you get my drift. The primary reason was to get Luke's attention, but maybe Vader also got information that he wanted from Han when he was in that vulnerable state. Han just didn't know what he'd revealed.
