It would have been interesting, how it would have developed further. Romans relied heavily on their disciplined infantry, while the Chinese have been famous in history for their foot & horse riding archers.The Han Dynasty led a expedition to permanently defeat the Hsiung-nu (HUN) tribes that constantly plaque the Silk road. Under Generals Ten Ku and Keng Ping very a large Hsiung-nu force was defeated. During this battle, a subordinate cavalry commander, Pan Ch'ao, was ordered by General Ten Ku to attack the Hu-yen, an allied tribe of the Hsiung-nu and subdue them. Pan Ch'ao easily accomplished this task and was sent with a primary light cavalry army to advance as far as possible to the West.
This expedition was to expand the Han Empire to its furthest western boundaries. The main purpose of the advance was to drive the defeated Hsiung-nu into Outer Mongolia.
Pan Ch'ao's army was composed of roughly equal amounts of Chinese regulars and Khotan auxiliaries, all apparently lance equipped horse archers, while the Chinese were heavy lance armed horse. Along the way the Wu-sun were picked up as allies. Pan Ch'ao also forced subdued states to furnish additional horse archers for his army. This force, was a very mobile one, with few, if any, infantry.
Turfan fell without a fight. With minor opposition here and there, By 73 CE Pan Ch'ao defeated all 36 kingdoms in and around the Tarim Basin.
Probably occurring in 90 A.D., dated by subsequent events that follow this battle, dated in Chavannes' T'oung Pao, as Pan Ch'ao had defeated all tribes and lands of the Tarim Basin no one had rescinded his orders, Pan Ch'ao continued his westward drive. As Pan Ch'ao was about to skirt the northern edge of the Pamirs Mountains, the Kushan (N. India) ruler saw that, unless an action was forced, his domain would be endangered.
A force of 70,000 cavalry was sent under Viceroy Si across the Tsung-ling Mountain range to intercept Pan Ch'ao. Unfortunately, this crossing was made at the wrong place at the wrong time of the year, and many died. Seriously damaged in strength, the Kushan Army emerged from the mountains shattered - but committed to fight. Pan Ch'ao easily defeated the depleted Kushan Army, and China received tribute from the Indian Kingdom.
By 97 CE Pan Ch'ao had defeated Ansi (the Arsacid Parthian Empire). Now Han China stood, the greatest land-owning empire only second to Rome. Pan Ch'ao ordered his second in command, Kan Ying, to set forth across newly conquered Ansi, to "Ta-ts'in", the Chinese name for the Roman Empire. Pan Ch'ao only allocated a portion of the army to subdue this "additional Kingdom", Kan Ying advanced across the middle Eastern expanses towards Antioch, thought to be the capitol of the Empire. Kan Ying was eager to know of his enemy, so the Parthians began to tell him about the legiones whose men fought "bundled up like little sticks" He also heard of the might and expanse of the Roman Empire. Upon gaining this new intelligence information, Kan Ying decided that his cavalry force was not sufficient for the task, and as he had no infantry he turned around and rejoined Pan Ch'ao at Ctesiphon. He was less then two days march from Antioch when he aborted. The Chinese army made the Parthians allies, and withdrew a days march from the capital. In 116 AD., Emperor Trajanus advances into Parthia to Ctesiphon and were within one day's march of Han Chinese border garrisons. But that's the closest the two came to blows.
As a side note, 97 A.D. was the first year of the Emperor Trajanus reign. It is quite interesting to speculate on the consequences had Kan Ying pursued his objective and attacked Roman Antioch.
It was the closest contact the Han and Romans ever came. (Granted the Han army was almost complete made up of allied horse archers)